(2g-2)4g-9=133

Solution for (2g-2)4g-9=133 equation:

(2g-2)4g-9=133

We move all terms to the left:

(2g-2)4g-9-(133)=0

We add all the numbers together, and all the variables

(2g-2)4g-142=0

We multiply parentheses

8g^2-8g-142=0

a = 8; b = -8; c = -142;
Δ = b2-4ac
Δ = -82-4·8·(-142)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-48\sqrt{2}}{2*8}=\frac{8-48\sqrt{2}}{16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+48\sqrt{2}}{2*8}=\frac{8+48\sqrt{2}}{16}
$