5x2-11x+7=8x2-20x+13

Solution for 5x2-11x+7=8x2-20x+13 equation:

5x^2-11x+7=8x^2-20x+13

We move all terms to the left:

5x^2-11x+7-(8x^2-20x+13)=0

We get rid of parentheses

5x^2-8x^2-11x+20x-13+7=0

We add all the numbers together, and all the variables

-3x^2+9x-6=0

a = -3; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-3)·(-6)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-3}=\frac{-6}{-6}
=1
$