25x^2-6x-49=0

Solution for 25x^2-6x-49=0 equation:

25x^2-6x-49=0

a = 25; b = -6; c = -49;
Δ = b2-4ac
Δ = -62-4·25·(-49)
Δ = 4936
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:

$\sqrt{\Delta}=\sqrt{4936}=\sqrt{4*1234}=\sqrt{4}*\sqrt{1234}=2\sqrt{1234}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1234}}{2*25}=\frac{6-2\sqrt{1234}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1234}}{2*25}=\frac{6+2\sqrt{1234}}{50}
$