3x*3x/2+43=139

Solution for 3x*3x/2+43=139 equation:

3x*3x/2+43=139

We move all terms to the left:

3x*3x/2+43-(139)=0

We add all the numbers together, and all the variables

3x*3x/2-96=0

We multiply all the terms by the denominator


3x*3x-96*2=0

We add all the numbers together, and all the variables

3x*3x-192=0

Wy multiply elements

9x^2-192=0

a = 9; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·9·(-192)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*9}=\frac{0-48\sqrt{3}}{18}
=-\frac{48\sqrt{3}}{18}
=-\frac{8\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*9}=\frac{0+48\sqrt{3}}{18}
=\frac{48\sqrt{3}}{18}
=\frac{8\sqrt{3}}{3}
$