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(2x+12)(3x+23)=0
We multiply parentheses ..
(+6x^2+46x+36x+276)=0
We get rid of parentheses
6x^2+46x+36x+276=0
We add all the numbers together, and all the variables
6x^2+82x+276=0
a = 6; b = 82; c = +276;
Δ = b2-4ac
Δ = 822-4·6·276
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-10}{2*6}=\frac{-92}{12} =-7+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+10}{2*6}=\frac{-72}{12} =-6 $
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