x+1/2x-5=85

Solution for x+1/2x-5=85 equation:

x+1/2x-5=85

We move all terms to the left:

x+1/2x-5-(85)=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+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 = 32392
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:

$\sqrt{\Delta}=\sqrt{32392}=\sqrt{4*8098}=\sqrt{4}*\sqrt{8098}=2\sqrt{8098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8098}}{2*2}=\frac{180-2\sqrt{8098}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8098}}{2*2}=\frac{180+2\sqrt{8098}}{4}
$