0=x^2+0,25x^2-8x^2+68

Solution for 0=x^2+0,25x^2-8x^2+68 equation:

0=x^2+0.25x^2-8x^2+68

We move all terms to the left:

0-(x^2+0.25x^2-8x^2+68)=0

We add all the numbers together, and all the variables

-(x^2+0.25x^2-8x^2+68)=0

We get rid of parentheses

-x^2-0.25x^2+8x^2-68=0

We add all the numbers together, and all the variables

6.75x^2-68=0

a = 6.75; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·6.75·(-68)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{51}}{2*6.75}=\frac{0-6\sqrt{51}}{13.5}
=-\frac{6\sqrt{51}}{13.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{51}}{2*6.75}=\frac{0+6\sqrt{51}}{13.5}
=\frac{6\sqrt{51}}{13.5}
$