-1/2x+5+(2x-7)=90

Solution for -1/2x+5+(2x-7)=90 equation:

-1/2x+5+(2x-7)=90

We move all terms to the left:

-1/2x+5+(2x-7)-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x+(2x-7)-85=0

We get rid of parentheses

-1/2x+2x-7-85=0

We multiply all the terms by the denominator


2x*2x-7*2x-85*2x-1=0

Wy multiply elements

4x^2-14x-170x-1=0

We add all the numbers together, and all the variables

4x^2-184x-1=0

a = 4; b = -184; c = -1;
Δ = b2-4ac
Δ = -1842-4·4·(-1)
Δ = 33872
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:

$\sqrt{\Delta}=\sqrt{33872}=\sqrt{16*2117}=\sqrt{16}*\sqrt{2117}=4\sqrt{2117}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-4\sqrt{2117}}{2*4}=\frac{184-4\sqrt{2117}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+4\sqrt{2117}}{2*4}=\frac{184+4\sqrt{2117}}{8}
$