(13x^2+11x-38)=0

Solution for (13x^2+11x-38)=0 equation:

(13x^2+11x-38)=0

We get rid of parentheses

13x^2+11x-38=0

a = 13; b = 11; c = -38;
Δ = b2-4ac
Δ = 112-4·13·(-38)
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{233}}{2*13}=\frac{-11-3\sqrt{233}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{233}}{2*13}=\frac{-11+3\sqrt{233}}{26}
$