c(2c-9)=5

Solution for c(2c-9)=5 equation:

c(2c-9)=5

We move all terms to the left:

c(2c-9)-(5)=0

We multiply parentheses

2c^2-9c-5=0

a = 2; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*2}=\frac{-2}{4}
=-1/2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*2}=\frac{20}{4}
=5
$