1/2x+90=x

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

1/2x+90=x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1x*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}
$