Question

solve the equation by factoring 6x^2-17x+13=20x^2-32

Answer 1

6x^2 - 17x+13 = 20x^2 - 32

14x^2 + 17x - 45 = 0

(2x + 5)(7x - 9) = 0

2x + 5 = 0

2x = -5

x = -5/2

7x - 9 = 0

7x = 9

x = 9/7

Answer

x = -5/2 , 9/7

Answer 2

Answer:

$x=\frac{-5}{2}$

$x=\frac{9}{7}$

Step-by-step explanation:

$6x^2-17x+13=20x^2-32$

combine like terms and simplify the equation

Subtract 6x^2 from both sides

$6x^2-17x+13=20x^2-32$

$-17x+13=14x^2-32$

Add 17x on both sides

$13=14x^2+17x-32$

Now subtract 13 from both sides

$0=14x^2+17x-45$

Now we solve for x

Apply quadratic formula : a= 14, b= +17 and c= -45

$x=\frac{-b+-\sqrt{b^2-4ac} }{2a}$

$x=\frac{-17+-\sqrt{17^2-4(14)(-45)} }{2(14)}$

$x=\frac{-17+-53}{28}$

Now make two equations

$x=\frac{-17+53}{28}=\frac{-5}{2}$

$x=\frac{-17-53}{28}=\frac{9}{7}$