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48x^2-54x=44
We move all terms to the left:
48x^2-54x-(44)=0
a = 48; b = -54; c = -44;
Δ = b2-4ac
Δ = -542-4·48·(-44)
Δ = 11364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11364}=\sqrt{4*2841}=\sqrt{4}*\sqrt{2841}=2\sqrt{2841}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{2841}}{2*48}=\frac{54-2\sqrt{2841}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{2841}}{2*48}=\frac{54+2\sqrt{2841}}{96} $
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