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6x(9x+30)=180
We move all terms to the left:
6x(9x+30)-(180)=0
We multiply parentheses
54x^2+180x-180=0
a = 54; b = 180; c = -180;
Δ = b2-4ac
Δ = 1802-4·54·(-180)
Δ = 71280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{71280}=\sqrt{1296*55}=\sqrt{1296}*\sqrt{55}=36\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-36\sqrt{55}}{2*54}=\frac{-180-36\sqrt{55}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+36\sqrt{55}}{2*54}=\frac{-180+36\sqrt{55}}{108} $
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