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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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-13}{2*12}=\frac{30}{24} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+13}{2*12}=\frac{56}{24} =2+1/3 $
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