(4x+11)(7x-6)=43

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Solution for (4x+11)(7x-6)=43 equation:



(4x+11)(7x-6)=43
We move all terms to the left:
(4x+11)(7x-6)-(43)=0
We multiply parentheses ..
(+28x^2-24x+77x-66)-43=0
We get rid of parentheses
28x^2-24x+77x-66-43=0
We add all the numbers together, and all the variables
28x^2+53x-109=0
a = 28; b = 53; c = -109;
Δ = b2-4ac
Δ = 532-4·28·(-109)
Δ = 15017
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{-(53)-\sqrt{15017}}{2*28}=\frac{-53-\sqrt{15017}}{56} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+\sqrt{15017}}{2*28}=\frac{-53+\sqrt{15017}}{56} $

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