11d^2-30d+13=0

Solution for 11d^2-30d+13=0 equation:

11d^2-30d+13=0

a = 11; b = -30; c = +13;
Δ = b2-4ac
Δ = -302-4·11·13
Δ = 328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{82}}{2*11}=\frac{30-2\sqrt{82}}{22}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{82}}{2*11}=\frac{30+2\sqrt{82}}{22}
$