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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

8x^2-987x=0

a = 8; b = -987; c = 0;
Δ = b2-4ac
Δ = -9872-4·8·0
Δ = 974169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{974169}=987$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-987)-987}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-987)+987}{2*8}=\frac{1974}{16}
=123+3/8
$