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(5x+6)(3x-4)=0
We multiply parentheses ..
(+15x^2-20x+18x-24)=0
We get rid of parentheses
15x^2-20x+18x-24=0
We add all the numbers together, and all the variables
15x^2-2x-24=0
a = 15; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·15·(-24)
Δ = 1444
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{1444}=38$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*15}=\frac{-36}{30} =-1+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*15}=\frac{40}{30} =1+1/3 $
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