34x+1x2=32

Solution for 34x+1x2=32 equation:

34x+1x^2=32

We move all terms to the left:

34x+1x^2-(32)=0

We add all the numbers together, and all the variables

x^2+34x-32=0

a = 1; b = 34; c = -32;
Δ = b2-4ac
Δ = 342-4·1·(-32)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{321}}{2*1}=\frac{-34-2\sqrt{321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{321}}{2*1}=\frac{-34+2\sqrt{321}}{2}
$