g^2-18g-88=35

Solution for g^2-18g-88=35 equation:

g^2-18g-88=35

We move all terms to the left:

g^2-18g-88-(35)=0

We add all the numbers together, and all the variables

g^2-18g-123=0

a = 1; b = -18; c = -123;
Δ = b2-4ac
Δ = -182-4·1·(-123)
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{51}}{2*1}=\frac{18-4\sqrt{51}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{51}}{2*1}=\frac{18+4\sqrt{51}}{2}
$