15X^2-26x+3=0

Solution for 15X^2-26x+3=0 equation:

15X^2-26X+3=0

a = 15; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·15·3
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-4\sqrt{31}}{2*15}=\frac{26-4\sqrt{31}}{30}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+4\sqrt{31}}{2*15}=\frac{26+4\sqrt{31}}{30}
$