7(u-5)9u=9u-45

Solution for 7(u-5)9u=9u-45 equation:

7(u-5)9u=9u-45

We move all terms to the left:

7(u-5)9u-(9u-45)=0

We multiply parentheses

63u^2-315u-(9u-45)=0

We get rid of parentheses

63u^2-315u-9u+45=0

We add all the numbers together, and all the variables

63u^2-324u+45=0

a = 63; b = -324; c = +45;
Δ = b2-4ac
Δ = -3242-4·63·45
Δ = 93636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{93636}=306$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-306}{2*63}=\frac{18}{126}
=1/7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+306}{2*63}=\frac{630}{126}
=5
$