3x^2-4x-51=0

Solution for 3x^2-4x-51=0 equation:

3x^2-4x-51=0

a = 3; b = -4; c = -51;
Δ = b2-4ac
Δ = -42-4·3·(-51)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{157}}{2*3}=\frac{4-2\sqrt{157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{157}}{2*3}=\frac{4+2\sqrt{157}}{6}
$