(2x-15)+(x+5)+(3/2x-5)+(12x+15)=100

Solution for (2x-15)+(x+5)+(3/2x-5)+(12x+15)=100 equation:

(2x-15)+(x+5)+(3/2x-5)+(12x+15)=100

We move all terms to the left:

(2x-15)+(x+5)+(3/2x-5)+(12x+15)-(100)=0


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

x∈R


We get rid of parentheses

2x+x+3/2x+12x-15+5-5+15-100=0

We multiply all the terms by the denominator


2x*2x+x*2x+12x*2x-15*2x+5*2x-5*2x+15*2x-100*2x+3=0

Wy multiply elements

4x^2+2x^2+24x^2-30x+10x-10x+30x-200x+3=0

We add all the numbers together, and all the variables

30x^2-200x+3=0

a = 30; b = -200; c = +3;
Δ = b2-4ac
Δ = -2002-4·30·3
Δ = 39640
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:

$\sqrt{\Delta}=\sqrt{39640}=\sqrt{4*9910}=\sqrt{4}*\sqrt{9910}=2\sqrt{9910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{9910}}{2*30}=\frac{200-2\sqrt{9910}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{9910}}{2*30}=\frac{200+2\sqrt{9910}}{60}
$