3(5x+2)7x=38

Solution for 3(5x+2)7x=38 equation:

3(5x+2)7x=38

We move all terms to the left:

3(5x+2)7x-(38)=0

We multiply parentheses

105x^2+42x-38=0

a = 105; b = 42; c = -38;
Δ = b2-4ac
Δ = 422-4·105·(-38)
Δ = 17724
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:

$\sqrt{\Delta}=\sqrt{17724}=\sqrt{4*4431}=\sqrt{4}*\sqrt{4431}=2\sqrt{4431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{4431}}{2*105}=\frac{-42-2\sqrt{4431}}{210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{4431}}{2*105}=\frac{-42+2\sqrt{4431}}{210}
$