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20-6x^2=20-
We move all terms to the left:
20-6x^2-(20-)=0
We add all the numbers together, and all the variables
-6x^2+20-0=0
We add all the numbers together, and all the variables
-6x^2+20=0
a = -6; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-6)·20
Δ = 480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-6}=\frac{0-4\sqrt{30}}{-12} =-\frac{4\sqrt{30}}{-12} =-\frac{\sqrt{30}}{-3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-6}=\frac{0+4\sqrt{30}}{-12} =\frac{4\sqrt{30}}{-12} =\frac{\sqrt{30}}{-3} $
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