u+12+u2+102u-17=180

Solution for u+12+u2+102u-17=180 equation:

u+12+u2+102u-17=180

We move all terms to the left:

u+12+u2+102u-17-(180)=0

We add all the numbers together, and all the variables

u^2+103u-185=0

a = 1; b = 103; c = -185;
Δ = b2-4ac
Δ = 1032-4·1·(-185)
Δ = 11349
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11349}=\sqrt{9*1261}=\sqrt{9}*\sqrt{1261}=3\sqrt{1261}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-3\sqrt{1261}}{2*1}=\frac{-103-3\sqrt{1261}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+3\sqrt{1261}}{2*1}=\frac{-103+3\sqrt{1261}}{2}
$