x^2=9-16x

Solution for x^2=9-16x equation:

x^2=9-16x

We move all terms to the left:

x^2-(9-16x)=0

We add all the numbers together, and all the variables

x^2-(-16x+9)=0

We get rid of parentheses

x^2+16x-9=0

a = 1; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·1·(-9)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{73}}{2*1}=\frac{-16-2\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{73}}{2*1}=\frac{-16+2\sqrt{73}}{2}
$