X=2t^2-9t+3

Solution for X=2t^2-9t+3 equation:

X=2X^2-9X+3

We move all terms to the left:

X-(2X^2-9X+3)=0

We get rid of parentheses

-2X^2+X+9X-3=0

We add all the numbers together, and all the variables

-2X^2+10X-3=0

a = -2; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-2)·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*-2}=\frac{-10-2\sqrt{19}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*-2}=\frac{-10+2\sqrt{19}}{-4}
$