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(2x-1)(3x-2)=38
We move all terms to the left:
(2x-1)(3x-2)-(38)=0
We multiply parentheses ..
(+6x^2-4x-3x+2)-38=0
We get rid of parentheses
6x^2-4x-3x+2-38=0
We add all the numbers together, and all the variables
6x^2-7x-36=0
a = 6; b = -7; c = -36;
Δ = b2-4ac
Δ = -72-4·6·(-36)
Δ = 913
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{913}}{2*6}=\frac{7-\sqrt{913}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{913}}{2*6}=\frac{7+\sqrt{913}}{12} $
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