4x^2+35x^2=9

Solution for 4x^2+35x^2=9 equation:

4x^2+35x^2=9

We move all terms to the left:

4x^2+35x^2-(9)=0

We add all the numbers together, and all the variables

39x^2-9=0

a = 39; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·39·(-9)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{39}}{2*39}=\frac{0-6\sqrt{39}}{78}
=-\frac{6\sqrt{39}}{78}
=-\frac{\sqrt{39}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{39}}{2*39}=\frac{0+6\sqrt{39}}{78}
=\frac{6\sqrt{39}}{78}
=\frac{\sqrt{39}}{13}
$