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6x^2-534=36x
We move all terms to the left:
6x^2-534-(36x)=0
a = 6; b = -36; c = -534;
Δ = b2-4ac
Δ = -362-4·6·(-534)
Δ = 14112
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14112}=\sqrt{7056*2}=\sqrt{7056}*\sqrt{2}=84\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-84\sqrt{2}}{2*6}=\frac{36-84\sqrt{2}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+84\sqrt{2}}{2*6}=\frac{36+84\sqrt{2}}{12} $
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