X=-1/2y+5

Solution for X=-1/2y+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 = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*2}=\frac{10-2\sqrt{23}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*2}=\frac{10+2\sqrt{23}}{4}
$