X^2+34x=120

Solution for X^2+34x=120 equation:

X^2+34X=120

We move all terms to the left:

X^2+34X-(120)=0

a = 1; b = 34; c = -120;
Δ = b2-4ac
Δ = 342-4·1·(-120)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{409}}{2*1}=\frac{-34-2\sqrt{409}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{409}}{2*1}=\frac{-34+2\sqrt{409}}{2}
$