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(6x-13)(3x+7)=0
We multiply parentheses ..
(+18x^2+42x-39x-91)=0
We get rid of parentheses
18x^2+42x-39x-91=0
We add all the numbers together, and all the variables
18x^2+3x-91=0
a = 18; b = 3; c = -91;
Δ = b2-4ac
Δ = 32-4·18·(-91)
Δ = 6561
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{6561}=81$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-81}{2*18}=\frac{-84}{36} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+81}{2*18}=\frac{78}{36} =2+1/6 $
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