# 15x(x+5)=150

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## Solution for 15x(x+5)=150 equation:

15x(x+5)=150
We move all terms to the left:
15x(x+5)-(150)=0
We multiply parentheses
15x^2+75x-150=0
a = 15; b = 75; c = -150;Δ = b2-4acΔ = 752-4·15·(-150)Δ = 14625The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{14625}=\sqrt{225*65}=\sqrt{225}*\sqrt{65}=15\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{65}}{2*15}=\frac{-75-15\sqrt{65}}{30}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{65}}{2*15}=\frac{-75+15\sqrt{65}}{30}$

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