5x(8x-11)=(2x+6)

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Solution for 5x(8x-11)=(2x+6) equation:



5x(8x-11)=(2x+6)
We move all terms to the left:
5x(8x-11)-((2x+6))=0
We multiply parentheses
40x^2-55x-((2x+6))=0
We calculate terms in parentheses: -((2x+6)), so:
(2x+6)
We get rid of parentheses
2x+6
Back to the equation:
-(2x+6)
We get rid of parentheses
40x^2-55x-2x-6=0
We add all the numbers together, and all the variables
40x^2-57x-6=0
a = 40; b = -57; c = -6;
Δ = b2-4ac
Δ = -572-4·40·(-6)
Δ = 4209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-\sqrt{4209}}{2*40}=\frac{57-\sqrt{4209}}{80} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{4209}}{2*40}=\frac{57+\sqrt{4209}}{80} $

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