9-2(4x+5)X=4

Solution for 9-2(4x+5)X=4 equation:

9-2(4x+5)x=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-8x^2-10x+5=0

a = -8; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·(-8)·5
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*-8}=\frac{10-2\sqrt{65}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*-8}=\frac{10+2\sqrt{65}}{-16}
$