25x^2+144x+196=0

Solution for 25x^2+144x+196=0 equation:

25x^2+144x+196=0

a = 25; b = 144; c = +196;
Δ = b2-4ac
Δ = 1442-4·25·196
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{71}}{2*25}=\frac{-144-4\sqrt{71}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{71}}{2*25}=\frac{-144+4\sqrt{71}}{50}
$