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288=3x^2-7x+3
We move all terms to the left:
288-(3x^2-7x+3)=0
We get rid of parentheses
-3x^2+7x-3+288=0
We add all the numbers together, and all the variables
-3x^2+7x+285=0
a = -3; b = 7; c = +285;
Δ = b2-4ac
Δ = 72-4·(-3)·285
Δ = 3469
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{3469}}{2*-3}=\frac{-7-\sqrt{3469}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{3469}}{2*-3}=\frac{-7+\sqrt{3469}}{-6} $
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