25x^2-40x-27=0

Solution for 25x^2-40x-27=0 equation:

25x^2-40x-27=0

a = 25; b = -40; c = -27;
Δ = b2-4ac
Δ = -402-4·25·(-27)
Δ = 4300
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:

$\sqrt{\Delta}=\sqrt{4300}=\sqrt{100*43}=\sqrt{100}*\sqrt{43}=10\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{43}}{2*25}=\frac{40-10\sqrt{43}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{43}}{2*25}=\frac{40+10\sqrt{43}}{50}
$