3x(x+24)=180

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Solution for 3x(x+24)=180 equation:



3x(x+24)=180
We move all terms to the left:
3x(x+24)-(180)=0
We multiply parentheses
3x^2+72x-180=0
a = 3; b = 72; c = -180;
Δ = b2-4ac
Δ = 722-4·3·(-180)
Δ = 7344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{51}}{2*3}=\frac{-72-12\sqrt{51}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{51}}{2*3}=\frac{-72+12\sqrt{51}}{6} $

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