4x2+16x+13=0

Solution for 4x2+16x+13=0 equation:

4x^2+16x+13=0

a = 4; b = 16; c = +13;
Δ = b2-4ac
Δ = 162-4·4·13
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{3}}{2*4}=\frac{-16-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{3}}{2*4}=\frac{-16+4\sqrt{3}}{8}
$