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(-3x+5)(4x-3)=0
We multiply parentheses ..
(-12x^2+9x+20x-15)=0
We get rid of parentheses
-12x^2+9x+20x-15=0
We add all the numbers together, and all the variables
-12x^2+29x-15=0
a = -12; b = 29; c = -15;
Δ = b2-4ac
Δ = 292-4·(-12)·(-15)
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-11}{2*-12}=\frac{-40}{-24} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*-12}=\frac{-18}{-24} =3/4 $
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