x(8-x)=7.5

Solution for x(8-x)=7.5 equation:

x(8-x)=7.5

We move all terms to the left:

x(8-x)-(7.5)=0

We add all the numbers together, and all the variables

x(-1x+8)-(7.5)=0

We add all the numbers together, and all the variables

x(-1x+8)-7.5=0

We multiply parentheses

-1x^2+8x-7.5=0

a = -1; b = 8; c = -7.5;
Δ = b2-4ac
Δ = 82-4·(-1)·(-7.5)
Δ = 34
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{-(8)-\sqrt{34}}{2*-1}=\frac{-8-\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+\sqrt{34}}{2*-1}=\frac{-8+\sqrt{34}}{-2}
$