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(5x+6)(3x+7)=0
We multiply parentheses ..
(+15x^2+35x+18x+42)=0
We get rid of parentheses
15x^2+35x+18x+42=0
We add all the numbers together, and all the variables
15x^2+53x+42=0
a = 15; b = 53; c = +42;
Δ = b2-4ac
Δ = 532-4·15·42
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-17}{2*15}=\frac{-70}{30} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+17}{2*15}=\frac{-36}{30} =-1+1/5 $
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