80-(4x^2+36x+80)=38.75

Solution for 80-(4x^2+36x+80)=38.75 equation:

80-(4x^2+36x+80)=38.75

We move all terms to the left:

80-(4x^2+36x+80)-(38.75)=0

We add all the numbers together, and all the variables

-(4x^2+36x+80)+41.25=0

We get rid of parentheses

-4x^2-36x-80+41.25=0

We add all the numbers together, and all the variables

-4x^2-36x-38.75=0

a = -4; b = -36; c = -38.75;
Δ = b2-4ac
Δ = -362-4·(-4)·(-38.75)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-26}{2*-4}=\frac{10}{-8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+26}{2*-4}=\frac{62}{-8}
=-7+3/4
$