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(2x+13)(x-7)=0
We multiply parentheses ..
(+2x^2-14x+13x-91)=0
We get rid of parentheses
2x^2-14x+13x-91=0
We add all the numbers together, and all the variables
2x^2-1x-91=0
a = 2; b = -1; c = -91;
Δ = b2-4ac
Δ = -12-4·2·(-91)
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-27}{2*2}=\frac{-26}{4} =-6+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+27}{2*2}=\frac{28}{4} =7 $
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