x-5=-5/2x+2

Solution for x-5=-5/2x+2 equation:

x-5=-5/2x+2

We move all terms to the left:

x-5-(-5/2x+2)=0


Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

x+5/2x-2-5=0

We multiply all the terms by the denominator


x*2x-2*2x-5*2x+5=0

Wy multiply elements

2x^2-4x-10x+5=0

We add all the numbers together, and all the variables

2x^2-14x+5=0

a = 2; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·2·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*2}=\frac{14-2\sqrt{39}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*2}=\frac{14+2\sqrt{39}}{4}
$