x^2+7x=32

Solution for x^2+7x=32 equation:

x^2+7x=32

We move all terms to the left:

x^2+7x-(32)=0

a = 1; b = 7; c = -32;
Δ = b2-4ac
Δ = 72-4·1·(-32)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{177}}{2*1}=\frac{-7-\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{177}}{2*1}=\frac{-7+\sqrt{177}}{2}
$