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4x^2=4x+44
We move all terms to the left:
4x^2-(4x+44)=0
We get rid of parentheses
4x^2-4x-44=0
a = 4; b = -4; c = -44;
Δ = b2-4ac
Δ = -42-4·4·(-44)
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{5}}{2*4}=\frac{4-12\sqrt{5}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{5}}{2*4}=\frac{4+12\sqrt{5}}{8} $
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