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 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 = 3440
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:

$\sqrt{\Delta}=\sqrt{3440}=\sqrt{16*215}=\sqrt{16}*\sqrt{215}=4\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{215}}{2*10}=\frac{-60-4\sqrt{215}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{215}}{2*10}=\frac{-60+4\sqrt{215}}{20}
$