4x2+8x2=1.5

Solution for 4x2+8x2=1.5 equation:

4x^2+8x^2=1.5

We move all terms to the left:

4x^2+8x^2-(1.5)=0

We add all the numbers together, and all the variables

12x^2-1.5=0

a = 12; b = 0; c = -1.5;
Δ = b2-4ac
Δ = 02-4·12·(-1.5)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*12}=\frac{0-6\sqrt{2}}{24}
=-\frac{6\sqrt{2}}{24}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*12}=\frac{0+6\sqrt{2}}{24}
=\frac{6\sqrt{2}}{24}
=\frac{\sqrt{2}}{4}
$