X^2-1+2x^2-4x+1=4x^2-22

Solution for X^2-1+2x^2-4x+1=4x^2-22 equation:

X^2-1+2X^2-4X+1=4X^2-22

We move all terms to the left:

X^2-1+2X^2-4X+1-(4X^2-22)=0

We add all the numbers together, and all the variables

3X^2-4X-(4X^2-22)=0

We get rid of parentheses

3X^2-4X^2-4X+22=0

We add all the numbers together, and all the variables

-1X^2-4X+22=0

a = -1; b = -4; c = +22;
Δ = b2-4ac
Δ = -42-4·(-1)·22
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{26}}{2*-1}=\frac{4-2\sqrt{26}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{26}}{2*-1}=\frac{4+2\sqrt{26}}{-2}
$