X+3/2x+90=180

Solution for X+3/2x+90=180 equation:

X+3/2X+90=180

We move all terms to the left:

X+3/2X+90-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

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}
$