X=2x^2-21x+19

Solution for X=2x^2-21x+19 equation:

X=2X^2-21X+19

We move all terms to the left:

X-(2X^2-21X+19)=0

We get rid of parentheses

-2X^2+X+21X-19=0

We add all the numbers together, and all the variables

-2X^2+22X-19=0

a = -2; b = 22; c = -19;
Δ = b2-4ac
Δ = 222-4·(-2)·(-19)
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{83}}{2*-2}=\frac{-22-2\sqrt{83}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{83}}{2*-2}=\frac{-22+2\sqrt{83}}{-4}
$