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(6x+7)(7x-13)=0
We multiply parentheses ..
(+42x^2-78x+49x-91)=0
We get rid of parentheses
42x^2-78x+49x-91=0
We add all the numbers together, and all the variables
42x^2-29x-91=0
a = 42; b = -29; c = -91;
Δ = b2-4ac
Δ = -292-4·42·(-91)
Δ = 16129
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{16129}=127$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-127}{2*42}=\frac{-98}{84} =-1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+127}{2*42}=\frac{156}{84} =1+6/7 $
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