x^2+0.75x^2=676

Solution for x^2+0.75x^2=676 equation:

x^2+0.75x^2=676

We move all terms to the left:

x^2+0.75x^2-(676)=0

We add all the numbers together, and all the variables

1.75x^2-676=0

a = 1.75; b = 0; c = -676;
Δ = b2-4ac
Δ = 02-4·1.75·(-676)
Δ = 4732
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:

$\sqrt{\Delta}=\sqrt{4732}=\sqrt{676*7}=\sqrt{676}*\sqrt{7}=26\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{7}}{2*1.75}=\frac{0-26\sqrt{7}}{3.5}
=-\frac{26\sqrt{7}}{3.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{7}}{2*1.75}=\frac{0+26\sqrt{7}}{3.5}
=\frac{26\sqrt{7}}{3.5}
$