X+5/4x=90

Solution for X+5/4x=90 equation:

X+5/4X=90

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4X^2-360X+5=0

a = 4; b = -360; c = +5;
Δ = b2-4ac
Δ = -3602-4·4·5
Δ = 129520
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:

$\sqrt{\Delta}=\sqrt{129520}=\sqrt{16*8095}=\sqrt{16}*\sqrt{8095}=4\sqrt{8095}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8095}}{2*4}=\frac{360-4\sqrt{8095}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8095}}{2*4}=\frac{360+4\sqrt{8095}}{8}
$