90-x=1/4x

Solution for 90-x=1/4x equation:

90-x=1/4x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 360; c = -1;
Δ = b2-4ac
Δ = 3602-4·(-4)·(-1)
Δ = 129584
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:

$\sqrt{\Delta}=\sqrt{129584}=\sqrt{16*8099}=\sqrt{16}*\sqrt{8099}=4\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-4\sqrt{8099}}{2*-4}=\frac{-360-4\sqrt{8099}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+4\sqrt{8099}}{2*-4}=\frac{-360+4\sqrt{8099}}{-8}
$