4x^2+6x^2=50

Solution for 4x^2+6x^2=50 equation:

4x^2+6x^2=50

We move all terms to the left:

4x^2+6x^2-(50)=0

We add all the numbers together, and all the variables

10x^2-50=0

a = 10; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·10·(-50)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*10}=\frac{0-20\sqrt{5}}{20}
=-\frac{20\sqrt{5}}{20}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*10}=\frac{0+20\sqrt{5}}{20}
=\frac{20\sqrt{5}}{20}
=\sqrt{5}
$