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500=4x*2x
We move all terms to the left:
500-(4x*2x)=0
We add all the numbers together, and all the variables
-(+4x*2x)+500=0
We get rid of parentheses
-4x*2x+500=0
Wy multiply elements
-8x^2+500=0
a = -8; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-8)·500
Δ = 16000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*-8}=\frac{0-40\sqrt{10}}{-16} =-\frac{40\sqrt{10}}{-16} =-\frac{5\sqrt{10}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*-8}=\frac{0+40\sqrt{10}}{-16} =\frac{40\sqrt{10}}{-16} =\frac{5\sqrt{10}}{-2} $
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