X=2x^2+20x-45

Solution for X=2x^2+20x-45 equation:

X=2X^2+20X-45

We move all terms to the left:

X-(2X^2+20X-45)=0

We get rid of parentheses

-2X^2+X-20X+45=0

We add all the numbers together, and all the variables

-2X^2-19X+45=0

a = -2; b = -19; c = +45;
Δ = b2-4ac
Δ = -192-4·(-2)·45
Δ = 721
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{-(-19)-\sqrt{721}}{2*-2}=\frac{19-\sqrt{721}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{721}}{2*-2}=\frac{19+\sqrt{721}}{-4}
$