3x^2+5x^2=4

Solution for 3x^2+5x^2=4 equation:

3x^2+5x^2=4

We move all terms to the left:

3x^2+5x^2-(4)=0

We add all the numbers together, and all the variables

8x^2-4=0

a = 8; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·8·(-4)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*8}=\frac{0-8\sqrt{2}}{16}
=-\frac{8\sqrt{2}}{16}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*8}=\frac{0+8\sqrt{2}}{16}
=\frac{8\sqrt{2}}{16}
=\frac{\sqrt{2}}{2}
$