X+(x+45)+90+(2x-90)+3/2x=540

Solution for X+(x+45)+90+(2x-90)+3/2x=540 equation:

X+(X+45)+90+(2X-90)+3/2X=540

We move all terms to the left:

X+(X+45)+90+(2X-90)+3/2X-(540)=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+(X+45)+(2X-90)+3/2X-450=0

We get rid of parentheses

X+X+2X+3/2X+45-90-450=0

We multiply all the terms by the denominator


X*2X+X*2X+2X*2X+45*2X-90*2X-450*2X+3=0

Wy multiply elements

2X^2+2X^2+4X^2+90X-180X-900X+3=0

We add all the numbers together, and all the variables

8X^2-990X+3=0

a = 8; b = -990; c = +3;
Δ = b2-4ac
Δ = -9902-4·8·3
Δ = 980004
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:

$\sqrt{\Delta}=\sqrt{980004}=\sqrt{4*245001}=\sqrt{4}*\sqrt{245001}=2\sqrt{245001}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-2\sqrt{245001}}{2*8}=\frac{990-2\sqrt{245001}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+2\sqrt{245001}}{2*8}=\frac{990+2\sqrt{245001}}{16}
$