0=-4x^2-14x+9

Solution for 0=-4x^2-14x+9 equation:

0=-4x^2-14x+9

We move all terms to the left:

0-(-4x^2-14x+9)=0

We add all the numbers together, and all the variables

-(-4x^2-14x+9)=0

We get rid of parentheses

4x^2+14x-9=0

a = 4; b = 14; c = -9;
Δ = b2-4ac
Δ = 142-4·4·(-9)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{85}}{2*4}=\frac{-14-2\sqrt{85}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{85}}{2*4}=\frac{-14+2\sqrt{85}}{8}
$