4/5x+18=-6-4x

Solution for 4/5x+18=-6-4x equation:

4/5x+18=-6-4x

We move all terms to the left:

4/5x+18-(-6-4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(-4x-6)+18=0

We get rid of parentheses

4/5x+4x+6+18=0

We multiply all the terms by the denominator


4x*5x+6*5x+18*5x+4=0

Wy multiply elements

20x^2+30x+90x+4=0

We add all the numbers together, and all the variables

20x^2+120x+4=0

a = 20; b = 120; c = +4;
Δ = b2-4ac
Δ = 1202-4·20·4
Δ = 14080
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:

$\sqrt{\Delta}=\sqrt{14080}=\sqrt{256*55}=\sqrt{256}*\sqrt{55}=16\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-16\sqrt{55}}{2*20}=\frac{-120-16\sqrt{55}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+16\sqrt{55}}{2*20}=\frac{-120+16\sqrt{55}}{40}
$