3(x2)-4(2x+5)=24

Solution for 3(x2)-4(2x+5)=24 equation:

3(x2)-4(2x+5)=24

We move all terms to the left:

3(x2)-4(2x+5)-(24)=0

We add all the numbers together, and all the variables

3x^2-4(2x+5)-24=0

We multiply parentheses

3x^2-8x-20-24=0

We add all the numbers together, and all the variables

3x^2-8x-44=0

a = 3; b = -8; c = -44;
Δ = b2-4ac
Δ = -82-4·3·(-44)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{37}}{2*3}=\frac{8-4\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{37}}{2*3}=\frac{8+4\sqrt{37}}{6}
$