3/2x+30+x=90

Solution for 3/2x+30+x=90 equation:

3/2x+30+x=90

We move all terms to the left:

3/2x+30+x-(90)=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-60=0

We multiply all the terms by the denominator


x*2x-60*2x+3=0

Wy multiply elements

2x^2-120x+3=0

a = 2; b = -120; c = +3;
Δ = b2-4ac
Δ = -1202-4·2·3
Δ = 14376
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:

$\sqrt{\Delta}=\sqrt{14376}=\sqrt{4*3594}=\sqrt{4}*\sqrt{3594}=2\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3594}}{2*2}=\frac{120-2\sqrt{3594}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3594}}{2*2}=\frac{120+2\sqrt{3594}}{4}
$