94x=24-8x^2

Solution for 94x=24-8x^2 equation:

94x=24-8x^2

We move all terms to the left:

94x-(24-8x^2)=0

We get rid of parentheses

8x^2+94x-24=0

a = 8; b = 94; c = -24;
Δ = b2-4ac
Δ = 942-4·8·(-24)
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(94)-98}{2*8}=\frac{-192}{16}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(94)+98}{2*8}=\frac{4}{16}
=1/4
$