3x^2-32x-69=0

Solution for 3x^2-32x-69=0 equation:

3x^2-32x-69=0

a = 3; b = -32; c = -69;
Δ = b2-4ac
Δ = -322-4·3·(-69)
Δ = 1852
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:

$\sqrt{\Delta}=\sqrt{1852}=\sqrt{4*463}=\sqrt{4}*\sqrt{463}=2\sqrt{463}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{463}}{2*3}=\frac{32-2\sqrt{463}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{463}}{2*3}=\frac{32+2\sqrt{463}}{6}
$