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(4x-1)(3x-7)=0
We multiply parentheses ..
(+12x^2-28x-3x+7)=0
We get rid of parentheses
12x^2-28x-3x+7=0
We add all the numbers together, and all the variables
12x^2-31x+7=0
a = 12; b = -31; c = +7;
Δ = b2-4ac
Δ = -312-4·12·7
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-25}{2*12}=\frac{6}{24} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+25}{2*12}=\frac{56}{24} =2+1/3 $
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