5x^2+4x^2=19

Solution for 5x^2+4x^2=19 equation:

5x^2+4x^2=19

We move all terms to the left:

5x^2+4x^2-(19)=0

We add all the numbers together, and all the variables

9x^2-19=0

a = 9; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·9·(-19)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*9}=\frac{0-6\sqrt{19}}{18}
=-\frac{6\sqrt{19}}{18}
=-\frac{\sqrt{19}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*9}=\frac{0+6\sqrt{19}}{18}
=\frac{6\sqrt{19}}{18}
=\frac{\sqrt{19}}{3}
$