x^2+1.5x^2-64=0

Solution for x^2+1.5x^2-64=0 equation:

x^2+1.5x^2-64=0

We add all the numbers together, and all the variables

2.5x^2-64=0

a = 2.5; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·2.5·(-64)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*2.5}=\frac{0-8\sqrt{10}}{5}
=-\frac{8\sqrt{10}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*2.5}=\frac{0+8\sqrt{10}}{5}
=\frac{8\sqrt{10}}{5}
$