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(5x+3)(6x+7)=0
We multiply parentheses ..
(+30x^2+35x+18x+21)=0
We get rid of parentheses
30x^2+35x+18x+21=0
We add all the numbers together, and all the variables
30x^2+53x+21=0
a = 30; b = 53; c = +21;
Δ = b2-4ac
Δ = 532-4·30·21
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-17}{2*30}=\frac{-70}{60} =-1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+17}{2*30}=\frac{-36}{60} =-3/5 $
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