5u(u-5)=-9u+37

Solution for 5u(u-5)=-9u+37 equation:

5u(u-5)=-9u+37

We move all terms to the left:

5u(u-5)-(-9u+37)=0

We multiply parentheses

5u^2-25u-(-9u+37)=0

We get rid of parentheses

5u^2-25u+9u-37=0

We add all the numbers together, and all the variables

5u^2-16u-37=0

a = 5; b = -16; c = -37;
Δ = b2-4ac
Δ = -162-4·5·(-37)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{249}}{2*5}=\frac{16-2\sqrt{249}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{249}}{2*5}=\frac{16+2\sqrt{249}}{10}
$