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(3x+5)(4x+6)=0
We multiply parentheses ..
(+12x^2+18x+20x+30)=0
We get rid of parentheses
12x^2+18x+20x+30=0
We add all the numbers together, and all the variables
12x^2+38x+30=0
a = 12; b = 38; c = +30;
Δ = b2-4ac
Δ = 382-4·12·30
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2}{2*12}=\frac{-40}{24} =-1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2}{2*12}=\frac{-36}{24} =-1+1/2 $
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