2x-12=4/5x

Solution for 2x-12=4/5x equation:

2x-12=4/5x

We move all terms to the left:

2x-12-(4/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-4/5x-12=0

We multiply all the terms by the denominator


2x*5x-12*5x-4=0

Wy multiply elements

10x^2-60x-4=0

a = 10; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·10·(-4)
Δ = 3760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{235}}{2*10}=\frac{60-4\sqrt{235}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{235}}{2*10}=\frac{60+4\sqrt{235}}{20}
$