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6x(2x-60)=180
We move all terms to the left:
6x(2x-60)-(180)=0
We multiply parentheses
12x^2-360x-180=0
a = 12; b = -360; c = -180;
Δ = b2-4ac
Δ = -3602-4·12·(-180)
Δ = 138240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{138240}=\sqrt{9216*15}=\sqrt{9216}*\sqrt{15}=96\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-96\sqrt{15}}{2*12}=\frac{360-96\sqrt{15}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+96\sqrt{15}}{2*12}=\frac{360+96\sqrt{15}}{24} $
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