X(2)-12=2x(2)-61

Solution for X(2)-12=2x(2)-61 equation:

X(2)-12=2X(2)-61

We move all terms to the left:

X(2)-12-(2X(2)-61)=0

We add all the numbers together, and all the variables

-(+2X^2-61)+X2-12=0

We add all the numbers together, and all the variables

X^2-(+2X^2-61)-12=0

We get rid of parentheses

X^2-2X^2+61-12=0

We add all the numbers together, and all the variables

-1X^2+49=0

a = -1; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-1)·49
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-1}=\frac{-14}{-2}
=+7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-1}=\frac{14}{-2}
=-7
$