40-(0.75*x)=x^2/20

Solution for 40-(0.75*x)=x^2/20 equation:

40-(0.75x)=x^2/20

We move all terms to the left:

40-(0.75x)-(x^2/20)=0

We add all the numbers together, and all the variables

-(+0.75x)-(x^2/20)+40=0

We get rid of parentheses

-x^2/20-0.75x+40=0

We multiply all the terms by the denominator


-x^2-(0.75x)*20+40*20=0

We add all the numbers together, and all the variables

-x^2-(+0.75x)*20+40*20=0

We add all the numbers together, and all the variables

-1x^2-(+0.75x)*20+800=0

We multiply parentheses

-1x^2-0x+800=0

We add all the numbers together, and all the variables

-1x^2-1x+800=0

a = -1; b = -1; c = +800;
Δ = b2-4ac
Δ = -12-4·(-1)·800
Δ = 3201
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{-(-1)-\sqrt{3201}}{2*-1}=\frac{1-\sqrt{3201}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3201}}{2*-1}=\frac{1+\sqrt{3201}}{-2}
$