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(3x-7)(4x-1)=8x-2
We move all terms to the left:
(3x-7)(4x-1)-(8x-2)=0
We get rid of parentheses
(3x-7)(4x-1)-8x+2=0
We multiply parentheses ..
(+12x^2-3x-28x+7)-8x+2=0
We get rid of parentheses
12x^2-3x-28x-8x+7+2=0
We add all the numbers together, and all the variables
12x^2-39x+9=0
a = 12; b = -39; c = +9;
Δ = b2-4ac
Δ = -392-4·12·9
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-33}{2*12}=\frac{6}{24} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+33}{2*12}=\frac{72}{24} =3 $
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