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(2x-3)3x-19=27
We move all terms to the left:
(2x-3)3x-19-(27)=0
We add all the numbers together, and all the variables
(2x-3)3x-46=0
We multiply parentheses
6x^2-9x-46=0
a = 6; b = -9; c = -46;
Δ = b2-4ac
Δ = -92-4·6·(-46)
Δ = 1185
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{-(-9)-\sqrt{1185}}{2*6}=\frac{9-\sqrt{1185}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{1185}}{2*6}=\frac{9+\sqrt{1185}}{12} $
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