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6x^2=7x+30
We move all terms to the left:
6x^2-(7x+30)=0
We get rid of parentheses
6x^2-7x-30=0
a = 6; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·6·(-30)
Δ = 769
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{769}}{2*6}=\frac{7-\sqrt{769}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{769}}{2*6}=\frac{7+\sqrt{769}}{12} $
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