X+(x+1/4x)=90

Solution for X+(x+1/4x)=90 equation:

X+(X+1/4X)=90

We move all terms to the left:

X+(X+1/4X)-(90)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+X+1/4X)-90=0

We get rid of parentheses

X+X+1/4X-90=0

We multiply all the terms by the denominator


X*4X+X*4X-90*4X+1=0

Wy multiply elements

4X^2+4X^2-360X+1=0

We add all the numbers together, and all the variables

8X^2-360X+1=0

a = 8; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·8·1
Δ = 129568
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:

$\sqrt{\Delta}=\sqrt{129568}=\sqrt{16*8098}=\sqrt{16}*\sqrt{8098}=4\sqrt{8098}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8098}}{2*8}=\frac{360-4\sqrt{8098}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8098}}{2*8}=\frac{360+4\sqrt{8098}}{16}
$