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6x^2-7=575
We move all terms to the left:
6x^2-7-(575)=0
We add all the numbers together, and all the variables
6x^2-582=0
a = 6; b = 0; c = -582;
Δ = b2-4ac
Δ = 02-4·6·(-582)
Δ = 13968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13968}=\sqrt{144*97}=\sqrt{144}*\sqrt{97}=12\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{97}}{2*6}=\frac{0-12\sqrt{97}}{12} =-\frac{12\sqrt{97}}{12} =-\sqrt{97} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{97}}{2*6}=\frac{0+12\sqrt{97}}{12} =\frac{12\sqrt{97}}{12} =\sqrt{97} $
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