5c^2-24c+11=0

Solution for 5c^2-24c+11=0 equation:

5c^2-24c+11=0

a = 5; b = -24; c = +11;
Δ = b2-4ac
Δ = -242-4·5·11
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{89}}{2*5}=\frac{24-2\sqrt{89}}{10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{89}}{2*5}=\frac{24+2\sqrt{89}}{10}
$