X^2+32x-274=0

Solution for X^2+32x-274=0 equation:

X^2+32X-274=0

a = 1; b = 32; c = -274;
Δ = b2-4ac
Δ = 322-4·1·(-274)
Δ = 2120
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:

$\sqrt{\Delta}=\sqrt{2120}=\sqrt{4*530}=\sqrt{4}*\sqrt{530}=2\sqrt{530}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{530}}{2*1}=\frac{-32-2\sqrt{530}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{530}}{2*1}=\frac{-32+2\sqrt{530}}{2}
$