1=5x^2-4x

Solution for 1=5x^2-4x equation:

1=5x^2-4x

We move all terms to the left:

1-(5x^2-4x)=0

We get rid of parentheses

-5x^2+4x+1=0

a = -5; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-5)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*-5}=\frac{2}{-10}
=-1/5
$