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6x^2+7x=12
We move all terms to the left:
6x^2+7x-(12)=0
a = 6; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·6·(-12)
Δ = 337
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{337}}{2*6}=\frac{-7-\sqrt{337}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{337}}{2*6}=\frac{-7+\sqrt{337}}{12} $
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