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x(x+2x)+20=180
We move all terms to the left:
x(x+2x)+20-(180)=0
We add all the numbers together, and all the variables
x(+3x)+20-180=0
We add all the numbers together, and all the variables
x(+3x)-160=0
We multiply parentheses
3x^2-160=0
a = 3; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·3·(-160)
Δ = 1920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*3}=\frac{0-8\sqrt{30}}{6} =-\frac{8\sqrt{30}}{6} =-\frac{4\sqrt{30}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*3}=\frac{0+8\sqrt{30}}{6} =\frac{8\sqrt{30}}{6} =\frac{4\sqrt{30}}{3} $
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