3x^2+32x+75=0

Solution for 3x^2+32x+75=0 equation:

3x^2+32x+75=0

a = 3; b = 32; c = +75;
Δ = b2-4ac
Δ = 322-4·3·75
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{31}}{2*3}=\frac{-32-2\sqrt{31}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{31}}{2*3}=\frac{-32+2\sqrt{31}}{6}
$