4f^2+47f-12=0

Solution for 4f^2+47f-12=0 equation:

4f^2+47f-12=0

a = 4; b = 47; c = -12;
Δ = b2-4ac
Δ = 472-4·4·(-12)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-49}{2*4}=\frac{-96}{8}
=-12
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+49}{2*4}=\frac{2}{8}
=1/4
$