4x^2/3-9=91

Solution for 4x^2/3-9=91 equation:

4x^2/3-9=91

We move all terms to the left:

4x^2/3-9-(91)=0

We add all the numbers together, and all the variables

4x^2/3-100=0

We multiply all the terms by the denominator


4x^2-100*3=0

We add all the numbers together, and all the variables

4x^2-300=0

a = 4; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·4·(-300)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*4}=\frac{0-40\sqrt{3}}{8}
=-\frac{40\sqrt{3}}{8}
=-5\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*4}=\frac{0+40\sqrt{3}}{8}
=\frac{40\sqrt{3}}{8}
=5\sqrt{3}
$