x=-1/2x+513

Solution for x=-1/2x+513 equation:

x=-1/2x+513

We move all terms to the left:

x-(-1/2x+513)=0


Domain of the equation: 2x+513)!=0

x∈R


We get rid of parentheses

x+1/2x-513=0

We multiply all the terms by the denominator


x*2x-513*2x+1=0

Wy multiply elements

2x^2-1026x+1=0

a = 2; b = -1026; c = +1;
Δ = b2-4ac
Δ = -10262-4·2·1
Δ = 1052668
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:

$\sqrt{\Delta}=\sqrt{1052668}=\sqrt{4*263167}=\sqrt{4}*\sqrt{263167}=2\sqrt{263167}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1026)-2\sqrt{263167}}{2*2}=\frac{1026-2\sqrt{263167}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1026)+2\sqrt{263167}}{2*2}=\frac{1026+2\sqrt{263167}}{4}
$