x+3/4x=90

Solution for x+3/4x=90 equation:

x+3/4x=90

We move all terms to the left:

x+3/4x-(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+3=0

Wy multiply elements

4x^2-360x+3=0

a = 4; b = -360; c = +3;
Δ = b2-4ac
Δ = -3602-4·4·3
Δ = 129552
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:

$\sqrt{\Delta}=\sqrt{129552}=\sqrt{16*8097}=\sqrt{16}*\sqrt{8097}=4\sqrt{8097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8097}}{2*4}=\frac{360-4\sqrt{8097}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8097}}{2*4}=\frac{360+4\sqrt{8097}}{8}
$