3X^2-26x+46=0

Solution for 3X^2-26x+46=0 equation:

3X^2-26X+46=0

a = 3; b = -26; c = +46;
Δ = b2-4ac
Δ = -262-4·3·46
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{-(-26)-2\sqrt{31}}{2*3}=\frac{26-2\sqrt{31}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{31}}{2*3}=\frac{26+2\sqrt{31}}{6}
$