0=3x^2-10x+7

Solution for 0=3x^2-10x+7 equation:

0=3x^2-10x+7

We move all terms to the left:

0-(3x^2-10x+7)=0

We add all the numbers together, and all the variables

-(3x^2-10x+7)=0

We get rid of parentheses

-3x^2+10x-7=0

a = -3; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·(-3)·(-7)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-3}=\frac{-6}{-6}
=1
$