(u+9)(13u-1)=u+9

Solution for (u+9)(13u-1)=u+9 equation:

(u+9)(13u-1)=u+9

We move all terms to the left:

(u+9)(13u-1)-(u+9)=0

We get rid of parentheses

(u+9)(13u-1)-u-9=0

We multiply parentheses ..

(+13u^2-1u+117u-9)-u-9=0

We add all the numbers together, and all the variables

(+13u^2-1u+117u-9)-1u-9=0

We get rid of parentheses

13u^2-1u+117u-1u-9-9=0

We add all the numbers together, and all the variables

13u^2+115u-18=0

a = 13; b = 115; c = -18;
Δ = b2-4ac
Δ = 1152-4·13·(-18)
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-119}{2*13}=\frac{-234}{26}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+119}{2*13}=\frac{4}{26}
=2/13
$