9(5x+12)7x=34

Solution for 9(5x+12)7x=34 equation:

9(5x+12)7x=34

We move all terms to the left:

9(5x+12)7x-(34)=0

We multiply parentheses

315x^2+756x-34=0

a = 315; b = 756; c = -34;
Δ = b2-4ac
Δ = 7562-4·315·(-34)
Δ = 614376
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:

$\sqrt{\Delta}=\sqrt{614376}=\sqrt{36*17066}=\sqrt{36}*\sqrt{17066}=6\sqrt{17066}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-6\sqrt{17066}}{2*315}=\frac{-756-6\sqrt{17066}}{630}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+6\sqrt{17066}}{2*315}=\frac{-756+6\sqrt{17066}}{630}
$