-5/8x+10x=-8

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

-5/8x+10x=-8

We move all terms to the left:

-5/8x+10x-(-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

10x-5/8x+8=0

We multiply all the terms by the denominator


10x*8x+8*8x-5=0

Wy multiply elements

80x^2+64x-5=0

a = 80; b = 64; c = -5;
Δ = b2-4ac
Δ = 642-4·80·(-5)
Δ = 5696
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:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{89}}{2*80}=\frac{-64-8\sqrt{89}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{89}}{2*80}=\frac{-64+8\sqrt{89}}{160}
$