(2x-6)(7x-7)=112

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Solution for (2x-6)(7x-7)=112 equation:



(2x-6)(7x-7)=112
We move all terms to the left:
(2x-6)(7x-7)-(112)=0
We multiply parentheses ..
(+14x^2-14x-42x+42)-112=0
We get rid of parentheses
14x^2-14x-42x+42-112=0
We add all the numbers together, and all the variables
14x^2-56x-70=0
a = 14; b = -56; c = -70;
Δ = b2-4ac
Δ = -562-4·14·(-70)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-84}{2*14}=\frac{-28}{28} =-1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+84}{2*14}=\frac{140}{28} =5 $

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