X=1/2x-5

Solution for X=1/2x-5 equation:

X=1/2X-5

We move all terms to the left:

X-(1/2X-5)=0


Domain of the equation: 2X-5)!=0

X∈R


We get rid of parentheses

X-1/2X+5=0

We multiply all the terms by the denominator


X*2X+5*2X-1=0

Wy multiply elements

2X^2+10X-1=0

a = 2; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·2·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{3}}{2*2}=\frac{-10-6\sqrt{3}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{3}}{2*2}=\frac{-10+6\sqrt{3}}{4}
$