3x^2-75x-48=0

Solution for 3x^2-75x-48=0 equation:

3x^2-75x-48=0

a = 3; b = -75; c = -48;
Δ = b2-4ac
Δ = -752-4·3·(-48)
Δ = 6201
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:

$\sqrt{\Delta}=\sqrt{6201}=\sqrt{9*689}=\sqrt{9}*\sqrt{689}=3\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-3\sqrt{689}}{2*3}=\frac{75-3\sqrt{689}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+3\sqrt{689}}{2*3}=\frac{75+3\sqrt{689}}{6}
$