-3x^2+52x-169=0

Solution for -3x^2+52x-169=0 equation:

-3x^2+52x-169=0

a = -3; b = 52; c = -169;
Δ = b2-4ac
Δ = 522-4·(-3)·(-169)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-26}{2*-3}=\frac{-78}{-6}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+26}{2*-3}=\frac{-26}{-6}
=4+1/3
$