SOLVING:
[tex]3X ^{2}+6X-7\quad\to\ Equalize\ the\ equation\ to\ zero.\\ \\3X ^{2}+6X-7=0[/tex]
The quadratic formula is: [tex]\boxed{X=\dfrac{-b\pm \sqrt{(b) ^{2}-4(a)(c) } }{2(a)}}[/tex]
Values:
a = 3
b = 6
c = - 7
STEPS:
[tex]X= \dfrac{-(6)\pm \sqrt{(6) ^{2}-4(3)(-7) } }{2(3)}\\ \\ \\X= \dfrac{-6\pm \sqrt{36+84} }{6}\\ \\ \\X= \dfrac{-6\pm \sqrt{120} }{6}\\ \\ \\X= \dfrac{-6\pm \sqrt{4*30} }{6}\\ \\ \\X= \dfrac{-6\pm \sqrt{2 ^{2}*30 } }{6}\\ \\ \\X= \dfrac{-6\pm2 \sqrt{30} }{6}[/tex]
Getting X₁:
[tex]X_{1}= \dfrac{-6+2 \sqrt{30} }{6}\to\ Factoring\ the\ numerator\ out\ common\ term\ 2.\\ \\ \\X_{1}= \dfrac{2(-3+1 \sqrt{30}) }{6}\to\ Reduce\ the\ common\ factor\ 2.\\ \\ \\X_{1}= \dfrac{-3+1 \sqrt{30} }{3}\\ \\ \\X_{1}=\boxed{ \boxed{ \dfrac{-3+ \sqrt{30} }{3} }}\quad\checkmark\ The\ first\ solution.[/tex]
Getting X₂:
[tex]X_{2}= \dfrac{-6-2 \sqrt{30} }{6}\to\ Factoring\ the\ numerator\ out\ common\ term\ 2.\\ \\ \\X_{2}= \dfrac{2(-3-1 \sqrt{30}) }{6}\to\ Reduce\ the\ common\ factor\ 2.\\ \\ \\X_{2}= \dfrac{-3-1 \sqrt{30} }{3}\\ \\ \\X_{2}=\boxed{ \boxed{ \dfrac{-3- \sqrt{30} }{3}}}\quad\checkmark\ The\ second\ solution.[/tex]
GOOD LUCK...!!
