4=5x^2-x

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

4=5x^2-x

We move all terms to the left:

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

We get rid of parentheses

-5x^2+x+4=0

a = -5; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-5)·4
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-5}=\frac{8}{-10}
=-4/5
$