(2x-15)+(x+5)+(3/2x-5)+(1/2x+15)=100

Solution for (2x-15)+(x+5)+(3/2x-5)+(1/2x+15)=100 equation:

(2x-15)+(x+5)+(3/2x-5)+(1/2x+15)=100

We move all terms to the left:

(2x-15)+(x+5)+(3/2x-5)+(1/2x+15)-(100)=0


Domain of the equation: 2x-5)!=0

x∈R



Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

2x+x+3/2x+1/2x-15+5-5+15-100=0

We multiply all the terms by the denominator


2x*2x+x*2x-15*2x+5*2x-5*2x+15*2x-100*2x+3+1=0

We add all the numbers together, and all the variables

2x*2x+x*2x-15*2x+5*2x-5*2x+15*2x-100*2x+4=0

Wy multiply elements

4x^2+2x^2-30x+10x-10x+30x-200x+4=0

We add all the numbers together, and all the variables

6x^2-200x+4=0

a = 6; b = -200; c = +4;
Δ = b2-4ac
Δ = -2002-4·6·4
Δ = 39904
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:

$\sqrt{\Delta}=\sqrt{39904}=\sqrt{16*2494}=\sqrt{16}*\sqrt{2494}=4\sqrt{2494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2494}}{2*6}=\frac{200-4\sqrt{2494}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2494}}{2*6}=\frac{200+4\sqrt{2494}}{12}
$