-4x^2=-16x-13

Solution for -4x^2=-16x-13 equation:

-4x^2=-16x-13

We move all terms to the left:

-4x^2-(-16x-13)=0

We get rid of parentheses

-4x^2+16x+13=0

a = -4; b = 16; c = +13;
Δ = b2-4ac
Δ = 162-4·(-4)·13
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{29}}{2*-4}=\frac{-16-4\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{29}}{2*-4}=\frac{-16+4\sqrt{29}}{-8}
$