3(x+4)7x=24

Solution for 3(x+4)7x=24 equation:

3(x+4)7x=24

We move all terms to the left:

3(x+4)7x-(24)=0

We multiply parentheses

21x^2+84x-24=0

a = 21; b = 84; c = -24;
Δ = b2-4ac
Δ = 842-4·21·(-24)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-36\sqrt{7}}{2*21}=\frac{-84-36\sqrt{7}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+36\sqrt{7}}{2*21}=\frac{-84+36\sqrt{7}}{42}
$