X2+32x-49=0

Solution for X2+32x-49=0 equation:

X2+32X-49=0

We add all the numbers together, and all the variables

X^2+32X-49=0

a = 1; b = 32; c = -49;
Δ = b2-4ac
Δ = 322-4·1·(-49)
Δ = 1220
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:

$\sqrt{\Delta}=\sqrt{1220}=\sqrt{4*305}=\sqrt{4}*\sqrt{305}=2\sqrt{305}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{305}}{2*1}=\frac{-32-2\sqrt{305}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{305}}{2*1}=\frac{-32+2\sqrt{305}}{2}
$