x2-5.78x-12.8=2.61

Solution for x2-5.78x-12.8=2.61 equation:

x2-5.78x-12.8=2.61

We move all terms to the left:

x2-5.78x-12.8-(2.61)=0

We add all the numbers together, and all the variables

x^2-5.78x-15.41=0

a = 1; b = -5.78; c = -15.41;
Δ = b2-4ac
Δ = -5.782-4·1·(-15.41)
Δ = 95.0484
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{-(-5.78)-\sqrt{95.0484}}{2*1}=\frac{5.78-\sqrt{95.0484}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.78)+\sqrt{95.0484}}{2*1}=\frac{5.78+\sqrt{95.0484}}{2}
$