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122x+4x^2=264
We move all terms to the left:
122x+4x^2-(264)=0
a = 4; b = 122; c = -264;
Δ = b2-4ac
Δ = 1222-4·4·(-264)
Δ = 19108
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19108}=\sqrt{4*4777}=\sqrt{4}*\sqrt{4777}=2\sqrt{4777}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-2\sqrt{4777}}{2*4}=\frac{-122-2\sqrt{4777}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+2\sqrt{4777}}{2*4}=\frac{-122+2\sqrt{4777}}{8} $
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