285=4x^2+56x+192

Solution for 285=4x^2+56x+192 equation:

285=4x^2+56x+192

We move all terms to the left:

285-(4x^2+56x+192)=0

We get rid of parentheses

-4x^2-56x-192+285=0

We add all the numbers together, and all the variables

-4x^2-56x+93=0

a = -4; b = -56; c = +93;
Δ = b2-4ac
Δ = -562-4·(-4)·93
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-68}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+68}{2*-4}=\frac{124}{-8}
=-15+1/2
$