0=-4x^2+10x-5

Solution for 0=-4x^2+10x-5 equation:

0=-4x^2+10x-5

We move all terms to the left:

0-(-4x^2+10x-5)=0

We add all the numbers together, and all the variables

-(-4x^2+10x-5)=0

We get rid of parentheses

4x^2-10x+5=0

a = 4; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·4·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*4}=\frac{10-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*4}=\frac{10+2\sqrt{5}}{8}
$