12x^2-292x+1390=0

Solution for 12x^2-292x+1390=0 equation:

12x^2-292x+1390=0

a = 12; b = -292; c = +1390;
Δ = b2-4ac
Δ = -2922-4·12·1390
Δ = 18544
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:

$\sqrt{\Delta}=\sqrt{18544}=\sqrt{16*1159}=\sqrt{16}*\sqrt{1159}=4\sqrt{1159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-292)-4\sqrt{1159}}{2*12}=\frac{292-4\sqrt{1159}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-292)+4\sqrt{1159}}{2*12}=\frac{292+4\sqrt{1159}}{24}
$