X^2+20x=460

Solution for X^2+20x=460 equation:

X^2+20X=460

We move all terms to the left:

X^2+20X-(460)=0

a = 1; b = 20; c = -460;
Δ = b2-4ac
Δ = 202-4·1·(-460)
Δ = 2240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{35}}{2*1}=\frac{-20-8\sqrt{35}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{35}}{2*1}=\frac{-20+8\sqrt{35}}{2}
$