6(8g(2)+2)+45=153

Solution for 6(8g(2)+2)+45=153 equation:

6(8g(2)+2)+45=153

We move all terms to the left:

6(8g(2)+2)+45-(153)=0

We add all the numbers together, and all the variables

6(+8g^2+2)+45-153=0

We add all the numbers together, and all the variables

6(+8g^2+2)-108=0

We multiply parentheses

48g^2+12-108=0

We add all the numbers together, and all the variables

48g^2-96=0

a = 48; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·48·(-96)
Δ = 18432
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:

$\sqrt{\Delta}=\sqrt{18432}=\sqrt{9216*2}=\sqrt{9216}*\sqrt{2}=96\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{2}}{2*48}=\frac{0-96\sqrt{2}}{96}
=-\frac{96\sqrt{2}}{96}
=-\sqrt{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{2}}{2*48}=\frac{0+96\sqrt{2}}{96}
=\frac{96\sqrt{2}}{96}
=\sqrt{2}
$