5x(x+6)=90

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Solution for 5x(x+6)=90 equation:



5x(x+6)=90
We move all terms to the left:
5x(x+6)-(90)=0
We multiply parentheses
5x^2+30x-90=0
a = 5; b = 30; c = -90;
Δ = b2-4ac
Δ = 302-4·5·(-90)
Δ = 2700
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:
$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{3}}{2*5}=\frac{-30-30\sqrt{3}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{3}}{2*5}=\frac{-30+30\sqrt{3}}{10} $

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