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3X^2-X+24=180
We move all terms to the left:
3X^2-X+24-(180)=0
We add all the numbers together, and all the variables
3X^2-1X-156=0
a = 3; b = -1; c = -156;
Δ = b2-4ac
Δ = -12-4·3·(-156)
Δ = 1873
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{-(-1)-\sqrt{1873}}{2*3}=\frac{1-\sqrt{1873}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1873}}{2*3}=\frac{1+\sqrt{1873}}{6} $
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