x=9/52x+32

Solution for x=9/52x+32 equation:

x=9/52x+32

We move all terms to the left:

x-(9/52x+32)=0


Domain of the equation: 52x+32)!=0

x∈R


We get rid of parentheses

x-9/52x-32=0

We multiply all the terms by the denominator


x*52x-32*52x-9=0

Wy multiply elements

52x^2-1664x-9=0

a = 52; b = -1664; c = -9;
Δ = b2-4ac
Δ = -16642-4·52·(-9)
Δ = 2770768
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:

$\sqrt{\Delta}=\sqrt{2770768}=\sqrt{16*173173}=\sqrt{16}*\sqrt{173173}=4\sqrt{173173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1664)-4\sqrt{173173}}{2*52}=\frac{1664-4\sqrt{173173}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1664)+4\sqrt{173173}}{2*52}=\frac{1664+4\sqrt{173173}}{104}
$