4x^2-3x^2-243=0

Solution for 4x^2-3x^2-243=0 equation:

4x^2-3x^2-243=0

We add all the numbers together, and all the variables

x^2-243=0

a = 1; b = 0; c = -243;
Δ = b2-4ac
Δ = 02-4·1·(-243)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*1}=\frac{0-18\sqrt{3}}{2}
=-\frac{18\sqrt{3}}{2}
=-9\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*1}=\frac{0+18\sqrt{3}}{2}
=\frac{18\sqrt{3}}{2}
=9\sqrt{3}
$