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(5x-4)(3x+7)=0
We multiply parentheses ..
(+15x^2+35x-12x-28)=0
We get rid of parentheses
15x^2+35x-12x-28=0
We add all the numbers together, and all the variables
15x^2+23x-28=0
a = 15; b = 23; c = -28;
Δ = b2-4ac
Δ = 232-4·15·(-28)
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-47}{2*15}=\frac{-70}{30} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+47}{2*15}=\frac{24}{30} =4/5 $
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