x^2+0.75x^2=225

Solution for x^2+0.75x^2=225 equation:

x^2+0.75x^2=225

We move all terms to the left:

x^2+0.75x^2-(225)=0

We add all the numbers together, and all the variables

1.75x^2-225=0

a = 1.75; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·1.75·(-225)
Δ = 1575
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:

$\sqrt{\Delta}=\sqrt{1575}=\sqrt{225*7}=\sqrt{225}*\sqrt{7}=15\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15\sqrt{7}}{2*1.75}=\frac{0-15\sqrt{7}}{3.5}
=-\frac{15\sqrt{7}}{3.5}
=-\frac{5\sqrt{7}}{1.16666666667}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15\sqrt{7}}{2*1.75}=\frac{0+15\sqrt{7}}{3.5}
=\frac{15\sqrt{7}}{3.5}
=\frac{5\sqrt{7}}{1.16666666667}
$