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(6x-6)(7x+1)=55
We move all terms to the left:
(6x-6)(7x+1)-(55)=0
We multiply parentheses ..
(+42x^2+6x-42x-6)-55=0
We get rid of parentheses
42x^2+6x-42x-6-55=0
We add all the numbers together, and all the variables
42x^2-36x-61=0
a = 42; b = -36; c = -61;
Δ = b2-4ac
Δ = -362-4·42·(-61)
Δ = 11544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11544}=\sqrt{4*2886}=\sqrt{4}*\sqrt{2886}=2\sqrt{2886}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{2886}}{2*42}=\frac{36-2\sqrt{2886}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{2886}}{2*42}=\frac{36+2\sqrt{2886}}{84} $
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