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x*0.2x=230
We move all terms to the left:
x*0.2x-(230)=0
Wy multiply elements
0x^2-230=0
We add all the numbers together, and all the variables
x^2-230=0
a = 1; b = 0; c = -230;
Δ = b2-4ac
Δ = 02-4·1·(-230)
Δ = 920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{230}}{2*1}=\frac{0-2\sqrt{230}}{2} =-\frac{2\sqrt{230}}{2} =-\sqrt{230} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{230}}{2*1}=\frac{0+2\sqrt{230}}{2} =\frac{2\sqrt{230}}{2} =\sqrt{230} $
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