3(2x+5)4x=7x-9

Solution for 3(2x+5)4x=7x-9 equation:

3(2x+5)4x=7x-9

We move all terms to the left:

3(2x+5)4x-(7x-9)=0

We multiply parentheses

24x^2+60x-(7x-9)=0

We get rid of parentheses

24x^2+60x-7x+9=0

We add all the numbers together, and all the variables

24x^2+53x+9=0

a = 24; b = 53; c = +9;
Δ = b2-4ac
Δ = 532-4·24·9
Δ = 1945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-\sqrt{1945}}{2*24}=\frac{-53-\sqrt{1945}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+\sqrt{1945}}{2*24}=\frac{-53+\sqrt{1945}}{48}
$