6x^2+11=25x

Solution for 6x^2+11=25x equation:

6x^2+11=25x

We move all terms to the left:

6x^2+11-(25x)=0

a = 6; b = -25; c = +11;
Δ = b2-4ac
Δ = -252-4·6·11
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-19}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+19}{2*6}=\frac{44}{12}
=3+2/3
$