-8+2.5x=5/2x-10

Solution for -8+2.5x=5/2x-10 equation:

-8+2.5x=5/2x-10

We move all terms to the left:

-8+2.5x-(5/2x-10)=0


Domain of the equation: 2x-10)!=0

x∈R


We get rid of parentheses

2.5x-5/2x+10-8=0

We multiply all the terms by the denominator


(2.5x)*2x+10*2x-8*2x-5=0

We add all the numbers together, and all the variables

(+2.5x)*2x+10*2x-8*2x-5=0

We multiply parentheses

4x^2+10*2x-8*2x-5=0

Wy multiply elements

4x^2+20x-16x-5=0

We add all the numbers together, and all the variables

4x^2+4x-5=0

a = 4; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·4·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*4}=\frac{-4-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*4}=\frac{-4+4\sqrt{6}}{8}
$