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5x(10x+15)=180
We move all terms to the left:
5x(10x+15)-(180)=0
We multiply parentheses
50x^2+75x-180=0
a = 50; b = 75; c = -180;
Δ = b2-4ac
Δ = 752-4·50·(-180)
Δ = 41625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41625}=\sqrt{225*185}=\sqrt{225}*\sqrt{185}=15\sqrt{185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{185}}{2*50}=\frac{-75-15\sqrt{185}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{185}}{2*50}=\frac{-75+15\sqrt{185}}{100} $
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