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3x(x+84)=180
We move all terms to the left:
3x(x+84)-(180)=0
We multiply parentheses
3x^2+252x-180=0
a = 3; b = 252; c = -180;
Δ = b2-4ac
Δ = 2522-4·3·(-180)
Δ = 65664
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{65664}=\sqrt{576*114}=\sqrt{576}*\sqrt{114}=24\sqrt{114}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-24\sqrt{114}}{2*3}=\frac{-252-24\sqrt{114}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+24\sqrt{114}}{2*3}=\frac{-252+24\sqrt{114}}{6} $
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