x(-3x+7)=3

Solution for x(-3x+7)=3 equation:

x(-3x+7)=3

We move all terms to the left:

x(-3x+7)-(3)=0

We multiply parentheses

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

a = -3; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-3)·(-3)
Δ = 13
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{-(7)-\sqrt{13}}{2*-3}=\frac{-7-\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{13}}{2*-3}=\frac{-7+\sqrt{13}}{-6}
$