3x^2-6x+7=5x+1

Solution for 3x^2-6x+7=5x+1 equation:

3x^2-6x+7=5x+1

We move all terms to the left:

3x^2-6x+7-(5x+1)=0

We get rid of parentheses

3x^2-6x-5x-1+7=0

We add all the numbers together, and all the variables

3x^2-11x+6=0

a = 3; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·3·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*3}=\frac{18}{6}
=3
$