9x2=72-7x2

Solution for 9x2=72-7x2 equation:

9x^2=72-7x^2

We move all terms to the left:

9x^2-(72-7x^2)=0

We get rid of parentheses

9x^2+7x^2-72=0

We add all the numbers together, and all the variables

16x^2-72=0

a = 16; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·16·(-72)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{2}}{2*16}=\frac{0-48\sqrt{2}}{32}
=-\frac{48\sqrt{2}}{32}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*16}=\frac{0+48\sqrt{2}}{32}
=\frac{48\sqrt{2}}{32}
=\frac{3\sqrt{2}}{2}
$