5x^2+3x^2=3+7

Solution for 5x^2+3x^2=3+7 equation:

5x^2+3x^2=3+7

We move all terms to the left:

5x^2+3x^2-(3+7)=0

We add all the numbers together, and all the variables

5x^2+3x^2-10=0

We add all the numbers together, and all the variables

8x^2-10=0

a = 8; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·8·(-10)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*8}=\frac{0-8\sqrt{5}}{16}
=-\frac{8\sqrt{5}}{16}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*8}=\frac{0+8\sqrt{5}}{16}
=\frac{8\sqrt{5}}{16}
=\frac{\sqrt{5}}{2}
$