3x^2+11=34x

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

3x^2+11=34x

We move all terms to the left:

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

a = 3; b = -34; c = +11;
Δ = b2-4ac
Δ = -342-4·3·11
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-32}{2*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+32}{2*3}=\frac{66}{6}
=11
$