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6x^2/5=11
We move all terms to the left:
6x^2/5-(11)=0
We multiply all the terms by the denominator
6x^2-11*5=0
We add all the numbers together, and all the variables
6x^2-55=0
a = 6; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·6·(-55)
Δ = 1320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{330}}{2*6}=\frac{0-2\sqrt{330}}{12} =-\frac{2\sqrt{330}}{12} =-\frac{\sqrt{330}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{330}}{2*6}=\frac{0+2\sqrt{330}}{12} =\frac{2\sqrt{330}}{12} =\frac{\sqrt{330}}{6} $
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