X=1/2x+50

Solution for X=1/2x+50 equation:

X=1/2X+50

We move all terms to the left:

X-(1/2X+50)=0


Domain of the equation: 2X+50)!=0

X∈R


We get rid of parentheses

X-1/2X-50=0

We multiply all the terms by the denominator


X*2X-50*2X-1=0

Wy multiply elements

2X^2-100X-1=0

a = 2; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·2·(-1)
Δ = 10008
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:

$\sqrt{\Delta}=\sqrt{10008}=\sqrt{36*278}=\sqrt{36}*\sqrt{278}=6\sqrt{278}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-6\sqrt{278}}{2*2}=\frac{100-6\sqrt{278}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+6\sqrt{278}}{2*2}=\frac{100+6\sqrt{278}}{4}
$