48z^2+76z+16=0

Solution for 48z^2+76z+16=0 equation:

48z^2+76z+16=0

a = 48; b = 76; c = +16;
Δ = b2-4ac
Δ = 762-4·48·16
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-52}{2*48}=\frac{-128}{96}
=-1+1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+52}{2*48}=\frac{-24}{96}
=-1/4
$