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(2x-7)(3x-1)=-7
We move all terms to the left:
(2x-7)(3x-1)-(-7)=0
We add all the numbers together, and all the variables
(2x-7)(3x-1)+7=0
We multiply parentheses ..
(+6x^2-2x-21x+7)+7=0
We get rid of parentheses
6x^2-2x-21x+7+7=0
We add all the numbers together, and all the variables
6x^2-23x+14=0
a = 6; b = -23; c = +14;
Δ = b2-4ac
Δ = -232-4·6·14
Δ = 193
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{-(-23)-\sqrt{193}}{2*6}=\frac{23-\sqrt{193}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{193}}{2*6}=\frac{23+\sqrt{193}}{12} $
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