4x^2+5x^2=90

Solution for 4x^2+5x^2=90 equation:

4x^2+5x^2=90

We move all terms to the left:

4x^2+5x^2-(90)=0

We add all the numbers together, and all the variables

9x^2-90=0

a = 9; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·9·(-90)
Δ = 3240
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:

$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{10}}{2*9}=\frac{0-18\sqrt{10}}{18}
=-\frac{18\sqrt{10}}{18}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{10}}{2*9}=\frac{0+18\sqrt{10}}{18}
=\frac{18\sqrt{10}}{18}
=\sqrt{10}
$