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(2x+7)(9x+6)=0
We multiply parentheses ..
(+18x^2+12x+63x+42)=0
We get rid of parentheses
18x^2+12x+63x+42=0
We add all the numbers together, and all the variables
18x^2+75x+42=0
a = 18; b = 75; c = +42;
Δ = b2-4ac
Δ = 752-4·18·42
Δ = 2601
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{2601}=51$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-51}{2*18}=\frac{-126}{36} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+51}{2*18}=\frac{-24}{36} =-2/3 $
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