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

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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} $

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