X=3x^2-150x+82

Solution for X=3x^2-150x+82 equation:

X=3X^2-150X+82

We move all terms to the left:

X-(3X^2-150X+82)=0

We get rid of parentheses

-3X^2+X+150X-82=0

We add all the numbers together, and all the variables

-3X^2+151X-82=0

a = -3; b = 151; c = -82;
Δ = b2-4ac
Δ = 1512-4·(-3)·(-82)
Δ = 21817
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{-(151)-\sqrt{21817}}{2*-3}=\frac{-151-\sqrt{21817}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(151)+\sqrt{21817}}{2*-3}=\frac{-151+\sqrt{21817}}{-6}
$