4x^2-51=51x

Solution for 4x^2-51=51x equation:

4x^2-51=51x

We move all terms to the left:

4x^2-51-(51x)=0

a = 4; b = -51; c = -51;
Δ = b2-4ac
Δ = -512-4·4·(-51)
Δ = 3417
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{-(-51)-\sqrt{3417}}{2*4}=\frac{51-\sqrt{3417}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{3417}}{2*4}=\frac{51+\sqrt{3417}}{8}
$