4x^2-6x+9=5x^2-6

Solution for 4x^2-6x+9=5x^2-6 equation:

4x^2-6x+9=5x^2-6

We move all terms to the left:

4x^2-6x+9-(5x^2-6)=0

We get rid of parentheses

4x^2-5x^2-6x+6+9=0

We add all the numbers together, and all the variables

-1x^2-6x+15=0

a = -1; b = -6; c = +15;
Δ = b2-4ac
Δ = -62-4·(-1)·15
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*-1}=\frac{6-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*-1}=\frac{6+4\sqrt{6}}{-2}
$