4x(6x-3)=92

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Solution for 4x(6x-3)=92 equation:



4x(6x-3)=92
We move all terms to the left:
4x(6x-3)-(92)=0
We multiply parentheses
24x^2-12x-92=0
a = 24; b = -12; c = -92;
Δ = b2-4ac
Δ = -122-4·24·(-92)
Δ = 8976
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:
$\sqrt{\Delta}=\sqrt{8976}=\sqrt{16*561}=\sqrt{16}*\sqrt{561}=4\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{561}}{2*24}=\frac{12-4\sqrt{561}}{48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{561}}{2*24}=\frac{12+4\sqrt{561}}{48} $

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