x+(4/5x-90)=90

Solution for x+(4/5x-90)=90 equation:

x+(4/5x-90)=90

We move all terms to the left:

x+(4/5x-90)-(90)=0


Domain of the equation: 5x-90)!=0

x∈R


We get rid of parentheses

x+4/5x-90-90=0

We multiply all the terms by the denominator


x*5x-90*5x-90*5x+4=0

Wy multiply elements

5x^2-450x-450x+4=0

We add all the numbers together, and all the variables

5x^2-900x+4=0

a = 5; b = -900; c = +4;
Δ = b2-4ac
Δ = -9002-4·5·4
Δ = 809920
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:

$\sqrt{\Delta}=\sqrt{809920}=\sqrt{64*12655}=\sqrt{64}*\sqrt{12655}=8\sqrt{12655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-8\sqrt{12655}}{2*5}=\frac{900-8\sqrt{12655}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+8\sqrt{12655}}{2*5}=\frac{900+8\sqrt{12655}}{10}
$