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(6x+1)(3x-7)=0
We multiply parentheses ..
(+18x^2-42x+3x-7)=0
We get rid of parentheses
18x^2-42x+3x-7=0
We add all the numbers together, and all the variables
18x^2-39x-7=0
a = 18; b = -39; c = -7;
Δ = b2-4ac
Δ = -392-4·18·(-7)
Δ = 2025
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{2025}=45$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-45}{2*18}=\frac{-6}{36} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+45}{2*18}=\frac{84}{36} =2+1/3 $
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