u2-13=7u

Solution for u2-13=7u equation:

u2-13=7u

We move all terms to the left:

u2-13-(7u)=0

We add all the numbers together, and all the variables

u^2-7u-13=0

a = 1; b = -7; c = -13;
Δ = b2-4ac
Δ = -72-4·1·(-13)
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{101}}{2*1}=\frac{7-\sqrt{101}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{101}}{2*1}=\frac{7+\sqrt{101}}{2}
$