x=1/2x+25

Solution for x=1/2x+25 equation:

x=1/2x+25

We move all terms to the left:

x-(1/2x+25)=0


Domain of the equation: 2x+25)!=0

x∈R


We get rid of parentheses

x-1/2x-25=0

We multiply all the terms by the denominator


x*2x-25*2x-1=0

Wy multiply elements

2x^2-50x-1=0

a = 2; b = -50; c = -1;
Δ = b2-4ac
Δ = -502-4·2·(-1)
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{627}}{2*2}=\frac{50-2\sqrt{627}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{627}}{2*2}=\frac{50+2\sqrt{627}}{4}
$