5(2x-17)9x=38

Solution for 5(2x-17)9x=38 equation:

5(2x-17)9x=38

We move all terms to the left:

5(2x-17)9x-(38)=0

We multiply parentheses

90x^2-765x-38=0

a = 90; b = -765; c = -38;
Δ = b2-4ac
Δ = -7652-4·90·(-38)
Δ = 598905
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:

$\sqrt{\Delta}=\sqrt{598905}=\sqrt{9*66545}=\sqrt{9}*\sqrt{66545}=3\sqrt{66545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-765)-3\sqrt{66545}}{2*90}=\frac{765-3\sqrt{66545}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-765)+3\sqrt{66545}}{2*90}=\frac{765+3\sqrt{66545}}{180}
$