X^2+16x-32=-7

Solution for X^2+16x-32=-7 equation:

X^2+16X-32=-7

We move all terms to the left:

X^2+16X-32-(-7)=0

We add all the numbers together, and all the variables

X^2+16X-25=0

a = 1; b = 16; c = -25;
Δ = b2-4ac
Δ = 162-4·1·(-25)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{89}}{2*1}=\frac{-16-2\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{89}}{2*1}=\frac{-16+2\sqrt{89}}{2}
$