X=10-3x2+6

Solution for X=10-3x2+6 equation:

X=10-3X^2+6

We move all terms to the left:

X-(10-3X^2+6)=0

We get rid of parentheses

3X^2+X-10-6=0

We add all the numbers together, and all the variables

3X^2+X-16=0

a = 3; b = 1; c = -16;
Δ = b2-4ac
Δ = 12-4·3·(-16)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{193}}{2*3}=\frac{-1-\sqrt{193}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*3}=\frac{-1+\sqrt{193}}{6}
$