0=5x^2+38x+48.5

Solution for 0=5x^2+38x+48.5 equation:

0=5x^2+38x+48.5

We move all terms to the left:

0-(5x^2+38x+48.5)=0

We add all the numbers together, and all the variables

-(5x^2+38x+48.5)=0

We get rid of parentheses

-5x^2-38x-48.5=0

a = -5; b = -38; c = -48.5;
Δ = b2-4ac
Δ = -382-4·(-5)·(-48.5)
Δ = 474
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{-(-38)-\sqrt{474}}{2*-5}=\frac{38-\sqrt{474}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+\sqrt{474}}{2*-5}=\frac{38+\sqrt{474}}{-10}
$