8/8x-10x=3x+25

Solution for 8/8x-10x=3x+25 equation:

8/8x-10x=3x+25

We move all terms to the left:

8/8x-10x-(3x+25)=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+8/8x-(3x+25)=0

We get rid of parentheses

-10x+8/8x-3x-25=0

We multiply all the terms by the denominator


-10x*8x-3x*8x-25*8x+8=0

Wy multiply elements

-80x^2-24x^2-200x+8=0

We add all the numbers together, and all the variables

-104x^2-200x+8=0

a = -104; b = -200; c = +8;
Δ = b2-4ac
Δ = -2002-4·(-104)·8
Δ = 43328
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:

$\sqrt{\Delta}=\sqrt{43328}=\sqrt{64*677}=\sqrt{64}*\sqrt{677}=8\sqrt{677}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{677}}{2*-104}=\frac{200-8\sqrt{677}}{-208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{677}}{2*-104}=\frac{200+8\sqrt{677}}{-208}
$