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(2x+7)(5x+6)=0
We multiply parentheses ..
(+10x^2+12x+35x+42)=0
We get rid of parentheses
10x^2+12x+35x+42=0
We add all the numbers together, and all the variables
10x^2+47x+42=0
a = 10; b = 47; c = +42;
Δ = b2-4ac
Δ = 472-4·10·42
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-23}{2*10}=\frac{-70}{20} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+23}{2*10}=\frac{-24}{20} =-1+1/5 $
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