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3x(2x+25)=180
We move all terms to the left:
3x(2x+25)-(180)=0
We multiply parentheses
6x^2+75x-180=0
a = 6; b = 75; c = -180;
Δ = b2-4ac
Δ = 752-4·6·(-180)
Δ = 9945
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9945}=\sqrt{9*1105}=\sqrt{9}*\sqrt{1105}=3\sqrt{1105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-3\sqrt{1105}}{2*6}=\frac{-75-3\sqrt{1105}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+3\sqrt{1105}}{2*6}=\frac{-75+3\sqrt{1105}}{12} $
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