0=4x^2+68x+51

Solution for 0=4x^2+68x+51 equation:

0=4x^2+68x+51

We move all terms to the left:

0-(4x^2+68x+51)=0

We add all the numbers together, and all the variables

-(4x^2+68x+51)=0

We get rid of parentheses

-4x^2-68x-51=0

a = -4; b = -68; c = -51;
Δ = b2-4ac
Δ = -682-4·(-4)·(-51)
Δ = 3808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{238}}{2*-4}=\frac{68-4\sqrt{238}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{238}}{2*-4}=\frac{68+4\sqrt{238}}{-8}
$