x=3x^2-10x+5

Solution for x=3x^2-10x+5 equation:

x=3x^2-10x+5

We move all terms to the left:

x-(3x^2-10x+5)=0

We get rid of parentheses

-3x^2+x+10x-5=0

We add all the numbers together, and all the variables

-3x^2+11x-5=0

a = -3; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-3)·(-5)
Δ = 61
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{-(11)-\sqrt{61}}{2*-3}=\frac{-11-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{61}}{2*-3}=\frac{-11+\sqrt{61}}{-6}
$