2x^2-90x=1

Solution for 2x^2-90x=1 equation:

2x^2-90x=1

We move all terms to the left:

2x^2-90x-(1)=0

a = 2; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·2·(-1)
Δ = 8108
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:

$\sqrt{\Delta}=\sqrt{8108}=\sqrt{4*2027}=\sqrt{4}*\sqrt{2027}=2\sqrt{2027}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2027}}{2*2}=\frac{90-2\sqrt{2027}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2027}}{2*2}=\frac{90+2\sqrt{2027}}{4}
$