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(5x+7)(3x+2)=0
We multiply parentheses ..
(+15x^2+10x+21x+14)=0
We get rid of parentheses
15x^2+10x+21x+14=0
We add all the numbers together, and all the variables
15x^2+31x+14=0
a = 15; b = 31; c = +14;
Δ = b2-4ac
Δ = 312-4·15·14
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-11}{2*15}=\frac{-42}{30} =-1+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+11}{2*15}=\frac{-20}{30} =-2/3 $
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