4x(x+2)-9=6x-8

Solution for 4x(x+2)-9=6x-8 equation:

4x(x+2)-9=6x-8

We move all terms to the left:

4x(x+2)-9-(6x-8)=0

We multiply parentheses

4x^2+8x-(6x-8)-9=0

We get rid of parentheses

4x^2+8x-6x+8-9=0

We add all the numbers together, and all the variables

4x^2+2x-1=0

a = 4; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·4·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*4}=\frac{-2-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*4}=\frac{-2+2\sqrt{5}}{8}
$