25x^2-105x=49

Solution for 25x^2-105x=49 equation:

25x^2-105x=49

We move all terms to the left:

25x^2-105x-(49)=0

a = 25; b = -105; c = -49;
Δ = b2-4ac
Δ = -1052-4·25·(-49)
Δ = 15925
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:

$\sqrt{\Delta}=\sqrt{15925}=\sqrt{1225*13}=\sqrt{1225}*\sqrt{13}=35\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-35\sqrt{13}}{2*25}=\frac{105-35\sqrt{13}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+35\sqrt{13}}{2*25}=\frac{105+35\sqrt{13}}{50}
$