x+8=-5/4x+2

Solution for x+8=-5/4x+2 equation:

x+8=-5/4x+2

We move all terms to the left:

x+8-(-5/4x+2)=0


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

x+5/4x-2+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-8x+32x+5=0

We add all the numbers together, and all the variables

4x^2+24x+5=0

a = 4; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·4·5
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{31}}{2*4}=\frac{-24-4\sqrt{31}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{31}}{2*4}=\frac{-24+4\sqrt{31}}{8}
$