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3x^2=7x+14
We move all terms to the left:
3x^2-(7x+14)=0
We get rid of parentheses
3x^2-7x-14=0
a = 3; b = -7; c = -14;
Δ = b2-4ac
Δ = -72-4·3·(-14)
Δ = 217
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{217}}{2*3}=\frac{7-\sqrt{217}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*3}=\frac{7+\sqrt{217}}{6} $
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