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3x^2-33x+30=7
We move all terms to the left:
3x^2-33x+30-(7)=0
We add all the numbers together, and all the variables
3x^2-33x+23=0
a = 3; b = -33; c = +23;
Δ = b2-4ac
Δ = -332-4·3·23
Δ = 813
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{-(-33)-\sqrt{813}}{2*3}=\frac{33-\sqrt{813}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{813}}{2*3}=\frac{33+\sqrt{813}}{6} $
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