2x^2-3x-20=x^2+34

Solution for 2x^2-3x-20=x^2+34 equation:

2x^2-3x-20=x^2+34

We move all terms to the left:

2x^2-3x-20-(x^2+34)=0

We get rid of parentheses

2x^2-x^2-3x-34-20=0

We add all the numbers together, and all the variables

x^2-3x-54=0

a = 1; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*1}=\frac{18}{2}
=9
$