-8(8-x)=4/5x+10

Solution for -8(8-x)=4/5x+10 equation:

-8(8-x)=4/5x+10

We move all terms to the left:

-8(8-x)-(4/5x+10)=0


Domain of the equation: 5x+10)!=0

x∈R


We add all the numbers together, and all the variables

-8(-1x+8)-(4/5x+10)=0

We multiply parentheses

8x-(4/5x+10)-64=0

We get rid of parentheses

8x-4/5x-10-64=0

We multiply all the terms by the denominator


8x*5x-10*5x-64*5x-4=0

Wy multiply elements

40x^2-50x-320x-4=0

We add all the numbers together, and all the variables

40x^2-370x-4=0

a = 40; b = -370; c = -4;
Δ = b2-4ac
Δ = -3702-4·40·(-4)
Δ = 137540
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:

$\sqrt{\Delta}=\sqrt{137540}=\sqrt{2116*65}=\sqrt{2116}*\sqrt{65}=46\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-370)-46\sqrt{65}}{2*40}=\frac{370-46\sqrt{65}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-370)+46\sqrt{65}}{2*40}=\frac{370+46\sqrt{65}}{80}
$