x*(5x-50)=150

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Solution for x*(5x-50)=150 equation:



x(5x-50)=150
We move all terms to the left:
x(5x-50)-(150)=0
We multiply parentheses
5x^2-50x-150=0
a = 5; b = -50; c = -150;
Δ = b2-4ac
Δ = -502-4·5·(-150)
Δ = 5500
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:
$\sqrt{\Delta}=\sqrt{5500}=\sqrt{100*55}=\sqrt{100}*\sqrt{55}=10\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{55}}{2*5}=\frac{50-10\sqrt{55}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{55}}{2*5}=\frac{50+10\sqrt{55}}{10} $

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