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(3x-4)(2x-9)=0
We multiply parentheses ..
(+6x^2-27x-8x+36)=0
We get rid of parentheses
6x^2-27x-8x+36=0
We add all the numbers together, and all the variables
6x^2-35x+36=0
a = 6; b = -35; c = +36;
Δ = b2-4ac
Δ = -352-4·6·36
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-19}{2*6}=\frac{16}{12} =1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+19}{2*6}=\frac{54}{12} =4+1/2 $
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