4x^2-109=35

Solution for 4x^2-109=35 equation:

4x^2-109=35

We move all terms to the left:

4x^2-109-(35)=0

We add all the numbers together, and all the variables

4x^2-144=0

a = 4; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·4·(-144)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*4}=\frac{48}{8}
=6
$