2.5x=x^2-8

Solution for 2.5x=x^2-8 equation:

2.5x=x^2-8

We move all terms to the left:

2.5x-(x^2-8)=0

We get rid of parentheses

-x^2+2.5x+8=0

We add all the numbers together, and all the variables

-1x^2+2.5x+8=0

a = -1; b = 2.5; c = +8;
Δ = b2-4ac
Δ = 2.52-4·(-1)·8
Δ = 38.25
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{-(2.5)-\sqrt{38.25}}{2*-1}=\frac{-2.5-\sqrt{38.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{38.25}}{2*-1}=\frac{-2.5+\sqrt{38.25}}{-2}
$