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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x-5/8x+18=0

We multiply all the terms by the denominator


x*8x+18*8x-5=0

Wy multiply elements

8x^2+144x-5=0

a = 8; b = 144; c = -5;
Δ = b2-4ac
Δ = 1442-4·8·(-5)
Δ = 20896
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:

$\sqrt{\Delta}=\sqrt{20896}=\sqrt{16*1306}=\sqrt{16}*\sqrt{1306}=4\sqrt{1306}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1306}}{2*8}=\frac{-144-4\sqrt{1306}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1306}}{2*8}=\frac{-144+4\sqrt{1306}}{16}
$