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(3x-5)(4x-7)=0
We multiply parentheses ..
(+12x^2-21x-20x+35)=0
We get rid of parentheses
12x^2-21x-20x+35=0
We add all the numbers together, and all the variables
12x^2-41x+35=0
a = 12; b = -41; c = +35;
Δ = b2-4ac
Δ = -412-4·12·35
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-1}{2*12}=\frac{40}{24} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+1}{2*12}=\frac{42}{24} =1+3/4 $
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