(3x)2-10/4=26

Solution for (3x)2-10/4=26 equation:

(3x)2-10/4=26

We move all terms to the left:

(3x)2-10/4-(26)=0

determiningTheFunctionDomain
3x2-26-10/4=0

We add all the numbers together, and all the variables

3x^2-26-10/4=0

We multiply all the terms by the denominator


3x^2*4-10-26*4=0

We add all the numbers together, and all the variables

3x^2*4-114=0

Wy multiply elements

12x^2-114=0

a = 12; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·12·(-114)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{38}}{2*12}=\frac{0-12\sqrt{38}}{24}
=-\frac{12\sqrt{38}}{24}
=-\frac{\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{38}}{2*12}=\frac{0+12\sqrt{38}}{24}
=\frac{12\sqrt{38}}{24}
=\frac{\sqrt{38}}{2}
$