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6x(5x+15)=180
We move all terms to the left:
6x(5x+15)-(180)=0
We multiply parentheses
30x^2+90x-180=0
a = 30; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·30·(-180)
Δ = 29700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29700}=\sqrt{900*33}=\sqrt{900}*\sqrt{33}=30\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-30\sqrt{33}}{2*30}=\frac{-90-30\sqrt{33}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+30\sqrt{33}}{2*30}=\frac{-90+30\sqrt{33}}{60} $
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