x^2+1,77x^2=6400

Solution for x^2+1,77x^2=6400 equation:

x^2+1.77x^2=6400

We move all terms to the left:

x^2+1.77x^2-(6400)=0

We add all the numbers together, and all the variables

2.77x^2-6400=0

a = 2.77; b = 0; c = -6400;
Δ = b2-4ac
Δ = 02-4·2.77·(-6400)
Δ = 70912
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:

$\sqrt{\Delta}=\sqrt{70912}=\sqrt{256*277}=\sqrt{256}*\sqrt{277}=16\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{277}}{2*2.77}=\frac{0-16\sqrt{277}}{5.54}
=-\frac{16\sqrt{277}}{5.54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{277}}{2*2.77}=\frac{0+16\sqrt{277}}{5.54}
=\frac{16\sqrt{277}}{5.54}
$