-4x^2-10x+9=5

Solution for -4x^2-10x+9=5 equation:

-4x^2-10x+9=5

We move all terms to the left:

-4x^2-10x+9-(5)=0

We add all the numbers together, and all the variables

-4x^2-10x+4=0

a = -4; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-4)·4
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{41}}{2*-4}=\frac{10-2\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{41}}{2*-4}=\frac{10+2\sqrt{41}}{-8}
$