51x^2-15x-39=0

Solution for 51x^2-15x-39=0 equation:

51x^2-15x-39=0

a = 51; b = -15; c = -39;
Δ = b2-4ac
Δ = -152-4·51·(-39)
Δ = 8181
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:

$\sqrt{\Delta}=\sqrt{8181}=\sqrt{81*101}=\sqrt{81}*\sqrt{101}=9\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9\sqrt{101}}{2*51}=\frac{15-9\sqrt{101}}{102}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9\sqrt{101}}{2*51}=\frac{15+9\sqrt{101}}{102}
$