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(3x+7)(4x+5)=0
We multiply parentheses ..
(+12x^2+15x+28x+35)=0
We get rid of parentheses
12x^2+15x+28x+35=0
We add all the numbers together, and all the variables
12x^2+43x+35=0
a = 12; b = 43; c = +35;
Δ = b2-4ac
Δ = 432-4·12·35
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-13}{2*12}=\frac{-56}{24} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+13}{2*12}=\frac{-30}{24} =-1+1/4 $
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