3x^2=-11x+34

Solution for 3x^2=-11x+34 equation:

3x^2=-11x+34

We move all terms to the left:

3x^2-(-11x+34)=0

We get rid of parentheses

3x^2+11x-34=0

a = 3; b = 11; c = -34;
Δ = b2-4ac
Δ = 112-4·3·(-34)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-23}{2*3}=\frac{-34}{6}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+23}{2*3}=\frac{12}{6}
=2
$