-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)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-5/8x+10=0

We multiply all the terms by the denominator


-1x*8x+10*8x-5=0

Wy multiply elements

-8x^2+80x-5=0

a = -8; b = 80; c = -5;
Δ = b2-4ac
Δ = 802-4·(-8)·(-5)
Δ = 6240
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:

$\sqrt{\Delta}=\sqrt{6240}=\sqrt{16*390}=\sqrt{16}*\sqrt{390}=4\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{390}}{2*-8}=\frac{-80-4\sqrt{390}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{390}}{2*-8}=\frac{-80+4\sqrt{390}}{-16}
$