x/5x-12=2x+6

Solution for x/5x-12=2x+6 equation:

x/5x-12=2x+6

We move all terms to the left:

x/5x-12-(2x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-2x-6-12=0

We multiply all the terms by the denominator


x-2x*5x-6*5x-12*5x=0

Wy multiply elements

-10x^2+x-30x-60x=0

We add all the numbers together, and all the variables

-10x^2-89x=0

a = -10; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·(-10)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*-10}=\frac{178}{-20}
=-8+9/10
$