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

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

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

We move all terms to the left:

4/5x+18-(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+12)+18=0

We get rid of parentheses

4/5x+4x-12+18=0

We multiply all the terms by the denominator


4x*5x-12*5x+18*5x+4=0

Wy multiply elements

20x^2-60x+90x+4=0

We add all the numbers together, and all the variables

20x^2+30x+4=0

a = 20; b = 30; c = +4;
Δ = b2-4ac
Δ = 302-4·20·4
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{145}}{2*20}=\frac{-30-2\sqrt{145}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{145}}{2*20}=\frac{-30+2\sqrt{145}}{40}
$