(X)=2x^2-9x+10

Solution for (X)=2x^2-9x+10 equation:

(X)=2X^2-9X+10

We move all terms to the left:

(X)-(2X^2-9X+10)=0

We get rid of parentheses

-2X^2+X+9X-10=0

We add all the numbers together, and all the variables

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

a = -2; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·(-2)·(-10)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*-2}=\frac{-10-2\sqrt{5}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*-2}=\frac{-10+2\sqrt{5}}{-4}
$