3x^2=-11x+13

Solution for 3x^2=-11x+13 equation:

3x^2=-11x+13

We move all terms to the left:

3x^2-(-11x+13)=0

We get rid of parentheses

3x^2+11x-13=0

a = 3; b = 11; c = -13;
Δ = b2-4ac
Δ = 112-4·3·(-13)
Δ = 277
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{-(11)-\sqrt{277}}{2*3}=\frac{-11-\sqrt{277}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{277}}{2*3}=\frac{-11+\sqrt{277}}{6}
$