3x2-7x=-3

Solution for 3x2-7x=-3 equation:

3x^2-7x=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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}
$