3x(x+5)-x-11=24

Solution for 3x(x+5)-x-11=24 equation:

3x(x+5)-x-11=24

We move all terms to the left:

3x(x+5)-x-11-(24)=0

We add all the numbers together, and all the variables

-1x+3x(x+5)-35=0

We multiply parentheses

3x^2-1x+15x-35=0

We add all the numbers together, and all the variables

3x^2+14x-35=0

a = 3; b = 14; c = -35;
Δ = b2-4ac
Δ = 142-4·3·(-35)
Δ = 616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{154}}{2*3}=\frac{-14-2\sqrt{154}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{154}}{2*3}=\frac{-14+2\sqrt{154}}{6}
$