48x=-3x^2-189

Solution for 48x=-3x^2-189 equation:

48x=-3x^2-189

We move all terms to the left:

48x-(-3x^2-189)=0

We get rid of parentheses

3x^2+48x+189=0

a = 3; b = 48; c = +189;
Δ = b2-4ac
Δ = 482-4·3·189
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6}{2*3}=\frac{-42}{6}
=-7
$