x=-1/2x+49

Solution for x=-1/2x+49 equation:

x=-1/2x+49

We move all terms to the left:

x-(-1/2x+49)=0


Domain of the equation: 2x+49)!=0

x∈R


We get rid of parentheses

x+1/2x-49=0

We multiply all the terms by the denominator


x*2x-49*2x+1=0

Wy multiply elements

2x^2-98x+1=0

a = 2; b = -98; c = +1;
Δ = b2-4ac
Δ = -982-4·2·1
Δ = 9596
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:

$\sqrt{\Delta}=\sqrt{9596}=\sqrt{4*2399}=\sqrt{4}*\sqrt{2399}=2\sqrt{2399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2399}}{2*2}=\frac{98-2\sqrt{2399}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2399}}{2*2}=\frac{98+2\sqrt{2399}}{4}
$