3/5g+12=-2+2g

Solution for 3/5g+12=-2+2g equation:

3/5g+12=-2+2g

We move all terms to the left:

3/5g+12-(-2+2g)=0


Domain of the equation: 5g!=0

g!=0/5

g!=0

g∈R


We add all the numbers together, and all the variables

3/5g-(2g-2)+12=0

We get rid of parentheses

3/5g-2g+2+12=0

We multiply all the terms by the denominator


-2g*5g+2*5g+12*5g+3=0

Wy multiply elements

-10g^2+10g+60g+3=0

We add all the numbers together, and all the variables

-10g^2+70g+3=0

a = -10; b = 70; c = +3;
Δ = b2-4ac
Δ = 702-4·(-10)·3
Δ = 5020
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:

$\sqrt{\Delta}=\sqrt{5020}=\sqrt{4*1255}=\sqrt{4}*\sqrt{1255}=2\sqrt{1255}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1255}}{2*-10}=\frac{-70-2\sqrt{1255}}{-20}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1255}}{2*-10}=\frac{-70+2\sqrt{1255}}{-20}
$