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(3x-4)(5x+3)=0
We multiply parentheses ..
(+15x^2+9x-20x-12)=0
We get rid of parentheses
15x^2+9x-20x-12=0
We add all the numbers together, and all the variables
15x^2-11x-12=0
a = 15; b = -11; c = -12;
Δ = b2-4ac
Δ = -112-4·15·(-12)
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*15}=\frac{-18}{30} =-3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*15}=\frac{40}{30} =1+1/3 $
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