-2g-12=3/4g-20

Solution for -2g-12=3/4g-20 equation:

-2g-12=3/4g-20

We move all terms to the left:

-2g-12-(3/4g-20)=0


Domain of the equation: 4g-20)!=0

g∈R


We get rid of parentheses

-2g-3/4g+20-12=0

We multiply all the terms by the denominator


-2g*4g+20*4g-12*4g-3=0

Wy multiply elements

-8g^2+80g-48g-3=0

We add all the numbers together, and all the variables

-8g^2+32g-3=0

a = -8; b = 32; c = -3;
Δ = b2-4ac
Δ = 322-4·(-8)·(-3)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{58}}{2*-8}=\frac{-32-4\sqrt{58}}{-16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{58}}{2*-8}=\frac{-32+4\sqrt{58}}{-16}
$