1.5625x^2-2.6x=-1

Solution for 1.5625x^2-2.6x=-1 equation:

1.5625x^2-2.6x=-1

We move all terms to the left:

1.5625x^2-2.6x-(-1)=0

We add all the numbers together, and all the variables

1.5625x^2-2.6x+1=0

a = 1.5625; b = -2.6; c = +1;
Δ = b2-4ac
Δ = -2.62-4·1.5625·1
Δ = 0.51
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.6)-\sqrt{0.51}}{2*1.5625}=\frac{2.6-\sqrt{0.51}}{3.125}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.6)+\sqrt{0.51}}{2*1.5625}=\frac{2.6+\sqrt{0.51}}{3.125}
$