4x2+48x+54=0

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Solution for 4x2+48x+54=0 equation:



4x^2+48x+54=0
a = 4; b = 48; c = +54;
Δ = b2-4ac
Δ = 482-4·4·54
Δ = 1440
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:
$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{10}}{2*4}=\frac{-48-12\sqrt{10}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{10}}{2*4}=\frac{-48+12\sqrt{10}}{8} $

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