x=90-3/2x

Solution for x=90-3/2x equation:

x=90-3/2x

We move all terms to the left:

x-(90-3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-3/2x+90)=0

We get rid of parentheses

x+3/2x-90=0

We multiply all the terms by the denominator


x*2x-90*2x+3=0

Wy multiply elements

2x^2-180x+3=0

a = 2; b = -180; c = +3;
Δ = b2-4ac
Δ = -1802-4·2·3
Δ = 32376
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:

$\sqrt{\Delta}=\sqrt{32376}=\sqrt{4*8094}=\sqrt{4}*\sqrt{8094}=2\sqrt{8094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8094}}{2*2}=\frac{180-2\sqrt{8094}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8094}}{2*2}=\frac{180+2\sqrt{8094}}{4}
$