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(3x+5)(2x+7)=0
We multiply parentheses ..
(+6x^2+21x+10x+35)=0
We get rid of parentheses
6x^2+21x+10x+35=0
We add all the numbers together, and all the variables
6x^2+31x+35=0
a = 6; b = 31; c = +35;
Δ = b2-4ac
Δ = 312-4·6·35
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-11}{2*6}=\frac{-42}{12} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+11}{2*6}=\frac{-20}{12} =-1+2/3 $
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