12(7x+5)x=13

Solution for 12(7x+5)x=13 equation:

12(7x+5)x=13

We move all terms to the left:

12(7x+5)x-(13)=0

We multiply parentheses

84x^2+60x-13=0

a = 84; b = 60; c = -13;
Δ = b2-4ac
Δ = 602-4·84·(-13)
Δ = 7968
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:

$\sqrt{\Delta}=\sqrt{7968}=\sqrt{16*498}=\sqrt{16}*\sqrt{498}=4\sqrt{498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{498}}{2*84}=\frac{-60-4\sqrt{498}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{498}}{2*84}=\frac{-60+4\sqrt{498}}{168}
$