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(4x+7)(6x+3)=0
We multiply parentheses ..
(+24x^2+12x+42x+21)=0
We get rid of parentheses
24x^2+12x+42x+21=0
We add all the numbers together, and all the variables
24x^2+54x+21=0
a = 24; b = 54; c = +21;
Δ = b2-4ac
Δ = 542-4·24·21
Δ = 900
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{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30}{2*24}=\frac{-84}{48} =-1+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30}{2*24}=\frac{-24}{48} =-1/2 $
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