13x^2-32x-92=0

Solution for 13x^2-32x-92=0 equation:

13x^2-32x-92=0

a = 13; b = -32; c = -92;
Δ = b2-4ac
Δ = -322-4·13·(-92)
Δ = 5808
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:

$\sqrt{\Delta}=\sqrt{5808}=\sqrt{1936*3}=\sqrt{1936}*\sqrt{3}=44\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-44\sqrt{3}}{2*13}=\frac{32-44\sqrt{3}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+44\sqrt{3}}{2*13}=\frac{32+44\sqrt{3}}{26}
$