90+x=1/2x

Solution for 90+x=1/2x equation:

90+x=1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-1/2x+90=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+180x-1=0

a = 2; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·2·(-1)
Δ = 32408
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:

$\sqrt{\Delta}=\sqrt{32408}=\sqrt{4*8102}=\sqrt{4}*\sqrt{8102}=2\sqrt{8102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8102}}{2*2}=\frac{-180-2\sqrt{8102}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8102}}{2*2}=\frac{-180+2\sqrt{8102}}{4}
$