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3x^2-7x-2=288
We move all terms to the left:
3x^2-7x-2-(288)=0
We add all the numbers together, and all the variables
3x^2-7x-290=0
a = 3; b = -7; c = -290;
Δ = b2-4ac
Δ = -72-4·3·(-290)
Δ = 3529
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{3529}}{2*3}=\frac{7-\sqrt{3529}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{3529}}{2*3}=\frac{7+\sqrt{3529}}{6} $
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