2500x^2-100x-15=1

Solution for 2500x^2-100x-15=1 equation:

2500x^2-100x-15=1

We move all terms to the left:

2500x^2-100x-15-(1)=0

We add all the numbers together, and all the variables

2500x^2-100x-16=0

a = 2500; b = -100; c = -16;
Δ = b2-4ac
Δ = -1002-4·2500·(-16)
Δ = 170000
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:

$\sqrt{\Delta}=\sqrt{170000}=\sqrt{10000*17}=\sqrt{10000}*\sqrt{17}=100\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100\sqrt{17}}{2*2500}=\frac{100-100\sqrt{17}}{5000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{17}}{2*2500}=\frac{100+100\sqrt{17}}{5000}
$