48x-0.8x^2=400

Solution for 48x-0.8x^2=400 equation:

48x-0.8x^2=400

We move all terms to the left:

48x-0.8x^2-(400)=0

a = -0.8; b = 48; c = -400;
Δ = b2-4ac
Δ = 482-4·(-0.8)·(-400)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-32}{2*-0.8}=\frac{-80}{-1.6}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+32}{2*-0.8}=\frac{-16}{-1.6}
=+10
$