-4x^2+16x+23=0

Solution for -4x^2+16x+23=0 equation:

-4x^2+16x+23=0

a = -4; b = 16; c = +23;
Δ = b2-4ac
Δ = 162-4·(-4)·23
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{39}}{2*-4}=\frac{-16-4\sqrt{39}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{39}}{2*-4}=\frac{-16+4\sqrt{39}}{-8}
$