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6x^2=2x+3
We move all terms to the left:
6x^2-(2x+3)=0
We get rid of parentheses
6x^2-2x-3=0
a = 6; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·6·(-3)
Δ = 76
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*6}=\frac{2-2\sqrt{19}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*6}=\frac{2+2\sqrt{19}}{12} $
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