2(-3x+5)8x=2x+10

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Solution for 2(-3x+5)8x=2x+10 equation:



2(-3x+5)8x=2x+10
We move all terms to the left:
2(-3x+5)8x-(2x+10)=0
We multiply parentheses
-48x^2+80x-(2x+10)=0
We get rid of parentheses
-48x^2+80x-2x-10=0
We add all the numbers together, and all the variables
-48x^2+78x-10=0
a = -48; b = 78; c = -10;
Δ = b2-4ac
Δ = 782-4·(-48)·(-10)
Δ = 4164
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:
$\sqrt{\Delta}=\sqrt{4164}=\sqrt{4*1041}=\sqrt{4}*\sqrt{1041}=2\sqrt{1041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1041}}{2*-48}=\frac{-78-2\sqrt{1041}}{-96} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1041}}{2*-48}=\frac{-78+2\sqrt{1041}}{-96} $

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