Question

Solve the following quadratic equation: 6x2 + 3x - 30 = 0

{1/2,7/5}

{3,-5/2}

{-1/3,5}

Answer 1

$6x^2+3x-30=0\ \ \ \ |:3\\\\2x^2+x-10=0\\\\2x^2+5x-4x-10=0\\\\x(2x+5)-2(2x+5)=0\\\\(2x+5)(x-2)=0\iff2x+5=0\ \vee\ x-2=0\\\\2x+5=0\ \ \ |-5\\2x=-5\ \ \ |:2\\x=-\frac{5}{2}\\\\x-2=0\ \ \ |+2\\x=2\\\\Answer:\ \left\{-\dfrac{5}{2};\ 2\right\}$