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(3x-4)(7x-9)=0
We multiply parentheses ..
(+21x^2-27x-28x+36)=0
We get rid of parentheses
21x^2-27x-28x+36=0
We add all the numbers together, and all the variables
21x^2-55x+36=0
a = 21; b = -55; c = +36;
Δ = b2-4ac
Δ = -552-4·21·36
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-1}{2*21}=\frac{54}{42} =1+2/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+1}{2*21}=\frac{56}{42} =1+1/3 $
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