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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-30x+100x+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}
$