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(3x+7)(5x-8)=0
We multiply parentheses ..
(+15x^2-24x+35x-56)=0
We get rid of parentheses
15x^2-24x+35x-56=0
We add all the numbers together, and all the variables
15x^2+11x-56=0
a = 15; b = 11; c = -56;
Δ = b2-4ac
Δ = 112-4·15·(-56)
Δ = 3481
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{3481}=59$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-59}{2*15}=\frac{-70}{30} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*15}=\frac{48}{30} =1+3/5 $
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