13y^2-42y-10=0

Solution for 13y^2-42y-10=0 equation:

13y^2-42y-10=0

a = 13; b = -42; c = -10;
Δ = b2-4ac
Δ = -422-4·13·(-10)
Δ = 2284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2284}=\sqrt{4*571}=\sqrt{4}*\sqrt{571}=2\sqrt{571}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{571}}{2*13}=\frac{42-2\sqrt{571}}{26}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{571}}{2*13}=\frac{42+2\sqrt{571}}{26}
$