x^2+15x-32=74

Solution for x^2+15x-32=74 equation:

x^2+15x-32=74

We move all terms to the left:

x^2+15x-32-(74)=0

We add all the numbers together, and all the variables

x^2+15x-106=0

a = 1; b = 15; c = -106;
Δ = b2-4ac
Δ = 152-4·1·(-106)
Δ = 649
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{-(15)-\sqrt{649}}{2*1}=\frac{-15-\sqrt{649}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{649}}{2*1}=\frac{-15+\sqrt{649}}{2}
$