15x^2-9x-48=0

Solution for 15x^2-9x-48=0 equation:

15x^2-9x-48=0

a = 15; b = -9; c = -48;
Δ = b2-4ac
Δ = -92-4·15·(-48)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{329}}{2*15}=\frac{9-3\sqrt{329}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{329}}{2*15}=\frac{9+3\sqrt{329}}{30}
$