5=10-10x+2.5x^2

Solution for 5=10-10x+2.5x^2 equation:

5=10-10x+2.5x^2

We move all terms to the left:

5-(10-10x+2.5x^2)=0

We get rid of parentheses

-2.5x^2+10x-10+5=0

We add all the numbers together, and all the variables

-2.5x^2+10x-5=0

a = -2.5; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-2.5)·(-5)
Δ = 50
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-5\sqrt{2}}{2*-2.5}=\frac{-10-5\sqrt{2}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+5\sqrt{2}}{2*-2.5}=\frac{-10+5\sqrt{2}}{-5}
$