x+(x+45)+(2x-90)+3/2x=459

Solution for x+(x+45)+(2x-90)+3/2x=459 equation:

x+(x+45)+(2x-90)+3/2x=459

We move all terms to the left:

x+(x+45)+(2x-90)+3/2x-(459)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+x+2x+3/2x+45-90-459=0

We multiply all the terms by the denominator


x*2x+x*2x+2x*2x+45*2x-90*2x-459*2x+3=0

Wy multiply elements

2x^2+2x^2+4x^2+90x-180x-918x+3=0

We add all the numbers together, and all the variables

8x^2-1008x+3=0

a = 8; b = -1008; c = +3;
Δ = b2-4ac
Δ = -10082-4·8·3
Δ = 1015968
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:

$\sqrt{\Delta}=\sqrt{1015968}=\sqrt{16*63498}=\sqrt{16}*\sqrt{63498}=4\sqrt{63498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63498}}{2*8}=\frac{1008-4\sqrt{63498}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63498}}{2*8}=\frac{1008+4\sqrt{63498}}{16}
$