X-5=-5/2y

Solution for X-5=-5/2y equation:

X-5=-5/2X

We move all terms to the left:

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


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We get rid of parentheses

X+5/2X-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2-10X+5=0

a = 2; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·2·5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*2}=\frac{10-2\sqrt{15}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*2}=\frac{10+2\sqrt{15}}{4}
$