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30x^2-6x-12=x
We move all terms to the left:
30x^2-6x-12-(x)=0
We add all the numbers together, and all the variables
30x^2-7x-12=0
a = 30; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·30·(-12)
Δ = 1489
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{1489}}{2*30}=\frac{7-\sqrt{1489}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1489}}{2*30}=\frac{7+\sqrt{1489}}{60} $
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