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

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

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

We get rid of parentheses

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
$