3x(5x+1)=48

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Solution for 3x(5x+1)=48 equation:



3x(5x+1)=48
We move all terms to the left:
3x(5x+1)-(48)=0
We multiply parentheses
15x^2+3x-48=0
a = 15; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·15·(-48)
Δ = 2889
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:
$\sqrt{\Delta}=\sqrt{2889}=\sqrt{9*321}=\sqrt{9}*\sqrt{321}=3\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{321}}{2*15}=\frac{-3-3\sqrt{321}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{321}}{2*15}=\frac{-3+3\sqrt{321}}{30} $

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