25x^2-78x-9=0

Solution for 25x^2-78x-9=0 equation:

25x^2-78x-9=0

a = 25; b = -78; c = -9;
Δ = b2-4ac
Δ = -782-4·25·(-9)
Δ = 6984
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:

$\sqrt{\Delta}=\sqrt{6984}=\sqrt{36*194}=\sqrt{36}*\sqrt{194}=6\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-6\sqrt{194}}{2*25}=\frac{78-6\sqrt{194}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+6\sqrt{194}}{2*25}=\frac{78+6\sqrt{194}}{50}
$