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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We use the square of the difference formula

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

We get rid of parentheses

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

a = -4; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-4)·4
Δ = 89
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{-(5)-\sqrt{89}}{2*-4}=\frac{-5-\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*-4}=\frac{-5+\sqrt{89}}{-8}
$