10x^2-8x=1

Solution for 10x^2-8x=1 equation:

10x^2-8x=1

We move all terms to the left:

10x^2-8x-(1)=0

a = 10; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·10·(-1)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*10}=\frac{8-2\sqrt{26}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*10}=\frac{8+2\sqrt{26}}{20}
$