0=5x^2+3x-4

Solution for 0=5x^2+3x-4 equation:

0=5x^2+3x-4

We move all terms to the left:

0-(5x^2+3x-4)=0

We add all the numbers together, and all the variables

-(5x^2+3x-4)=0

We get rid of parentheses

-5x^2-3x+4=0

a = -5; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-5)·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{-(-3)-\sqrt{89}}{2*-5}=\frac{3-\sqrt{89}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*-5}=\frac{3+\sqrt{89}}{-10}
$