4x(172+6x)=148

Solution for 4x(172+6x)=148 equation:

4x(172+6x)=148

We move all terms to the left:

4x(172+6x)-(148)=0

We add all the numbers together, and all the variables

4x(6x+172)-148=0

We multiply parentheses

24x^2+688x-148=0

a = 24; b = 688; c = -148;
Δ = b2-4ac
Δ = 6882-4·24·(-148)
Δ = 487552
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:

$\sqrt{\Delta}=\sqrt{487552}=\sqrt{64*7618}=\sqrt{64}*\sqrt{7618}=8\sqrt{7618}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(688)-8\sqrt{7618}}{2*24}=\frac{-688-8\sqrt{7618}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(688)+8\sqrt{7618}}{2*24}=\frac{-688+8\sqrt{7618}}{48}
$