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(3x+4)(8x-6)=0
We multiply parentheses ..
(+24x^2-18x+32x-24)=0
We get rid of parentheses
24x^2-18x+32x-24=0
We add all the numbers together, and all the variables
24x^2+14x-24=0
a = 24; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·24·(-24)
Δ = 2500
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{2500}=50$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-50}{2*24}=\frac{-64}{48} =-1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+50}{2*24}=\frac{36}{48} =3/4 $
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