X=10-2(2x^2-16x+3)

Solution for X=10-2(2x^2-16x+3) equation:

X=10-2(2X^2-16X+3)

We move all terms to the left:

X-(10-2(2X^2-16X+3))=0


We calculate terms in parentheses: -(10-2(2X^2-16X+3)), so:

10-2(2X^2-16X+3)

determiningTheFunctionDomain
-2(2X^2-16X+3)+10

We multiply parentheses

-4X^2+32X-6+10

We add all the numbers together, and all the variables

-4X^2+32X+4

Back to the equation:

-(-4X^2+32X+4)


We get rid of parentheses

4X^2-32X+X-4=0

We add all the numbers together, and all the variables

4X^2-31X-4=0

a = 4; b = -31; c = -4;
Δ = b2-4ac
Δ = -312-4·4·(-4)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-5\sqrt{41}}{2*4}=\frac{31-5\sqrt{41}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+5\sqrt{41}}{2*4}=\frac{31+5\sqrt{41}}{8}
$