-64+8x=4/5x+8

Solution for -64+8x=4/5x+8 equation:

-64+8x=4/5x+8

We move all terms to the left:

-64+8x-(4/5x+8)=0


Domain of the equation: 5x+8)!=0

x∈R


We get rid of parentheses

8x-4/5x-8-64=0

We multiply all the terms by the denominator


8x*5x-8*5x-64*5x-4=0

Wy multiply elements

40x^2-40x-320x-4=0

We add all the numbers together, and all the variables

40x^2-360x-4=0

a = 40; b = -360; c = -4;
Δ = b2-4ac
Δ = -3602-4·40·(-4)
Δ = 130240
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:

$\sqrt{\Delta}=\sqrt{130240}=\sqrt{64*2035}=\sqrt{64}*\sqrt{2035}=8\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-8\sqrt{2035}}{2*40}=\frac{360-8\sqrt{2035}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+8\sqrt{2035}}{2*40}=\frac{360+8\sqrt{2035}}{80}
$