2c(c-3)=11(4)

Solution for 2c(c-3)=11(4) equation:

2c(c-3)=11(4)

We move all terms to the left:

2c(c-3)-(11(4))=0

determiningTheFunctionDomain
2c(c-3)-114=0

We multiply parentheses

2c^2-6c-114=0

a = 2; b = -6; c = -114;
Δ = b2-4ac
Δ = -62-4·2·(-114)
Δ = 948
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{237}}{2*2}=\frac{6-2\sqrt{237}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{237}}{2*2}=\frac{6+2\sqrt{237}}{4}
$