25x^2-6x=1=-16X

Solution for 25x^2-6x=1=-16X equation:

25x^2-6x=1=-16x

We move all terms to the left:

25x^2-6x-(1)=0

a = 25; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·25·(-1)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{34}}{2*25}=\frac{6-2\sqrt{34}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{34}}{2*25}=\frac{6+2\sqrt{34}}{50}
$