4x^2-37x^2+9=0

Solution for 4x^2-37x^2+9=0 equation:

4x^2-37x^2+9=0

We add all the numbers together, and all the variables

-33x^2+9=0

a = -33; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-33)·9
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{33}}{2*-33}=\frac{0-6\sqrt{33}}{-66}
=-\frac{6\sqrt{33}}{-66}
=-\frac{\sqrt{33}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{33}}{2*-33}=\frac{0+6\sqrt{33}}{-66}
=\frac{6\sqrt{33}}{-66}
=\frac{\sqrt{33}}{-11}
$