55-32x+3x^2=0

Solution for 55-32x+3x^2=0 equation:

55-32x+3x^2=0

a = 3; b = -32; c = +55;
Δ = b2-4ac
Δ = -322-4·3·55
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{91}}{2*3}=\frac{32-2\sqrt{91}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{91}}{2*3}=\frac{32+2\sqrt{91}}{6}
$