(2x-50)+(1/2x+15)=90

Solution for (2x-50)+(1/2x+15)=90 equation:

(2x-50)+(1/2x+15)=90

We move all terms to the left:

(2x-50)+(1/2x+15)-(90)=0


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

x∈R


We get rid of parentheses

2x+1/2x-50+15-90=0

We multiply all the terms by the denominator


2x*2x-50*2x+15*2x-90*2x+1=0

Wy multiply elements

4x^2-100x+30x-180x+1=0

We add all the numbers together, and all the variables

4x^2-250x+1=0

a = 4; b = -250; c = +1;
Δ = b2-4ac
Δ = -2502-4·4·1
Δ = 62484
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:

$\sqrt{\Delta}=\sqrt{62484}=\sqrt{4*15621}=\sqrt{4}*\sqrt{15621}=2\sqrt{15621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{15621}}{2*4}=\frac{250-2\sqrt{15621}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{15621}}{2*4}=\frac{250+2\sqrt{15621}}{8}
$