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(2x+7)(3x-17)=0
We multiply parentheses ..
(+6x^2-34x+21x-119)=0
We get rid of parentheses
6x^2-34x+21x-119=0
We add all the numbers together, and all the variables
6x^2-13x-119=0
a = 6; b = -13; c = -119;
Δ = b2-4ac
Δ = -132-4·6·(-119)
Δ = 3025
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{3025}=55$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-55}{2*6}=\frac{-42}{12} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+55}{2*6}=\frac{68}{12} =5+2/3 $
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