x^2+0.75x^2=19^2

Solution for x^2+0.75x^2=19^2 equation:

x^2+0.75x^2=19^2

We move all terms to the left:

x^2+0.75x^2-(19^2)=0

We add all the numbers together, and all the variables

1.75x^2-361=0

a = 1.75; b = 0; c = -361;
Δ = b2-4ac
Δ = 02-4·1.75·(-361)
Δ = 2527
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:

$\sqrt{\Delta}=\sqrt{2527}=\sqrt{361*7}=\sqrt{361}*\sqrt{7}=19\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-19\sqrt{7}}{2*1.75}=\frac{0-19\sqrt{7}}{3.5}
=-\frac{19\sqrt{7}}{3.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+19\sqrt{7}}{2*1.75}=\frac{0+19\sqrt{7}}{3.5}
=\frac{19\sqrt{7}}{3.5}
$