2x^2-69x+20=7x^2-8

Solution for 2x^2-69x+20=7x^2-8 equation:

2x^2-69x+20=7x^2-8

We move all terms to the left:

2x^2-69x+20-(7x^2-8)=0

We get rid of parentheses

2x^2-7x^2-69x+8+20=0

We add all the numbers together, and all the variables

-5x^2-69x+28=0

a = -5; b = -69; c = +28;
Δ = b2-4ac
Δ = -692-4·(-5)·28
Δ = 5321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-\sqrt{5321}}{2*-5}=\frac{69-\sqrt{5321}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{5321}}{2*-5}=\frac{69+\sqrt{5321}}{-10}
$