x^2+18x-10=-75

Solution for x^2+18x-10=-75 equation:

x^2+18x-10=-75

We move all terms to the left:

x^2+18x-10-(-75)=0

We add all the numbers together, and all the variables

x^2+18x+65=0

a = 1; b = 18; c = +65;
Δ = b2-4ac
Δ = 182-4·1·65
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8}{2*1}=\frac{-10}{2}
=-5
$