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(3x-2)(2x)=31
We move all terms to the left:
(3x-2)(2x)-(31)=0
We multiply parentheses
6x^2-4x-31=0
a = 6; b = -4; c = -31;
Δ = b2-4ac
Δ = -42-4·6·(-31)
Δ = 760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{190}}{2*6}=\frac{4-2\sqrt{190}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{190}}{2*6}=\frac{4+2\sqrt{190}}{12} $
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