0=-1.2x^2+3.84x+177.69

Solution for 0=-1.2x^2+3.84x+177.69 equation:

0=-1.2x^2+3.84x+177.69

We move all terms to the left:

0-(-1.2x^2+3.84x+177.69)=0

We add all the numbers together, and all the variables

-(-1.2x^2+3.84x+177.69)=0

We get rid of parentheses

1.2x^2-3.84x-177.69=0

a = 1.2; b = -3.84; c = -177.69;
Δ = b2-4ac
Δ = -3.842-4·1.2·(-177.69)
Δ = 867.6576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3.84)-\sqrt{867.6576}}{2*1.2}=\frac{3.84-\sqrt{867.6576}}{2.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.84)+\sqrt{867.6576}}{2*1.2}=\frac{3.84+\sqrt{867.6576}}{2.4}
$