6x^2-11x+7=3

Solution for 6x^2-11x+7=3 equation:

6x^2-11x+7=3

We move all terms to the left:

6x^2-11x+7-(3)=0

We add all the numbers together, and all the variables

6x^2-11x+4=0

a = 6; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·6·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*6}=\frac{16}{12}
=1+1/3
$