10x^2+32x+12=0

Solution for 10x^2+32x+12=0 equation:

10x^2+32x+12=0

a = 10; b = 32; c = +12;
Δ = b2-4ac
Δ = 322-4·10·12
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{34}}{2*10}=\frac{-32-4\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{34}}{2*10}=\frac{-32+4\sqrt{34}}{20}
$