X=1/2x+57

Solution for X=1/2x+57 equation:

X=1/2X+57

We move all terms to the left:

X-(1/2X+57)=0


Domain of the equation: 2X+57)!=0

X∈R


We get rid of parentheses

X-1/2X-57=0

We multiply all the terms by the denominator


X*2X-57*2X-1=0

Wy multiply elements

2X^2-114X-1=0

a = 2; b = -114; c = -1;
Δ = b2-4ac
Δ = -1142-4·2·(-1)
Δ = 13004
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:

$\sqrt{\Delta}=\sqrt{13004}=\sqrt{4*3251}=\sqrt{4}*\sqrt{3251}=2\sqrt{3251}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3251}}{2*2}=\frac{114-2\sqrt{3251}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3251}}{2*2}=\frac{114+2\sqrt{3251}}{4}
$