x+5/2x+10=90

Solution for x+5/2x+10=90 equation:

x+5/2x+10=90

We move all terms to the left:

x+5/2x+10-(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

x+5/2x-80=0

We multiply all the terms by the denominator


x*2x-80*2x+5=0

Wy multiply elements

2x^2-160x+5=0

a = 2; b = -160; c = +5;
Δ = b2-4ac
Δ = -1602-4·2·5
Δ = 25560
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:

$\sqrt{\Delta}=\sqrt{25560}=\sqrt{36*710}=\sqrt{36}*\sqrt{710}=6\sqrt{710}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-6\sqrt{710}}{2*2}=\frac{160-6\sqrt{710}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+6\sqrt{710}}{2*2}=\frac{160+6\sqrt{710}}{4}
$