4x^2+5x^2=20^2

Solution for 4x^2+5x^2=20^2 equation:

4x^2+5x^2=20^2

We move all terms to the left:

4x^2+5x^2-(20^2)=0

We add all the numbers together, and all the variables

9x^2-400=0

a = 9; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·9·(-400)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*9}=\frac{-120}{18}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*9}=\frac{120}{18}
=6+2/3
$