38.88=7x+1.375x^2

Solution for 38.88=7x+1.375x^2 equation:

38.88=7x+1.375x^2

We move all terms to the left:

38.88-(7x+1.375x^2)=0

We get rid of parentheses

-1.375x^2-7x+38.88=0

a = -1.375; b = -7; c = +38.88;
Δ = b2-4ac
Δ = -72-4·(-1.375)·38.88
Δ = 262.84
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{-(-7)-\sqrt{262.84}}{2*-1.375}=\frac{7-\sqrt{262.84}}{-2.75}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{262.84}}{2*-1.375}=\frac{7+\sqrt{262.84}}{-2.75}
$