2/5g+4=g+12

Solution for 2/5g+4=g+12 equation:

2/5g+4=g+12

We move all terms to the left:

2/5g+4-(g+12)=0


Domain of the equation: 5g!=0

g!=0/5

g!=0

g∈R


We get rid of parentheses

2/5g-g-12+4=0

We multiply all the terms by the denominator


-g*5g-12*5g+4*5g+2=0

Wy multiply elements

-5g^2-60g+20g+2=0

We add all the numbers together, and all the variables

-5g^2-40g+2=0

a = -5; b = -40; c = +2;
Δ = b2-4ac
Δ = -402-4·(-5)·2
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{410}}{2*-5}=\frac{40-2\sqrt{410}}{-10}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{410}}{2*-5}=\frac{40+2\sqrt{410}}{-10}
$