(x2-3)2-5(x2-3)+6=0

Solution for (x2-3)2-5(x2-3)+6=0 equation:

(x2-3)2-5(x2-3)+6=0

We add all the numbers together, and all the variables

(+x^2-3)2-5(+x^2-3)+6=0

We multiply parentheses

2x^2-5x^2-6+15+6=0

We add all the numbers together, and all the variables

-3x^2+15=0

a = -3; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-3)·15
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-3}=\frac{0-6\sqrt{5}}{-6}
=-\frac{6\sqrt{5}}{-6}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-3}=\frac{0+6\sqrt{5}}{-6}
=\frac{6\sqrt{5}}{-6}
=\frac{\sqrt{5}}{-1}
$