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6x^2-12-4x=19x+32
We move all terms to the left:
6x^2-12-4x-(19x+32)=0
We get rid of parentheses
6x^2-4x-19x-32-12=0
We add all the numbers together, and all the variables
6x^2-23x-44=0
a = 6; b = -23; c = -44;
Δ = b2-4ac
Δ = -232-4·6·(-44)
Δ = 1585
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{-(-23)-\sqrt{1585}}{2*6}=\frac{23-\sqrt{1585}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1585}}{2*6}=\frac{23+\sqrt{1585}}{12} $
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