5(2x-3)=3(4x-5)2x

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

5(2x-3)=3(4x-5)2x

We move all terms to the left:

5(2x-3)-(3(4x-5)2x)=0

We multiply parentheses

10x-(3(4x-5)2x)-15=0


We calculate terms in parentheses: -(3(4x-5)2x), so:

3(4x-5)2x

We multiply parentheses

24x^2-30x

Back to the equation:

-(24x^2-30x)


We get rid of parentheses

-24x^2+10x+30x-15=0

We add all the numbers together, and all the variables

-24x^2+40x-15=0

a = -24; b = 40; c = -15;
Δ = b2-4ac
Δ = 402-4·(-24)·(-15)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{10}}{2*-24}=\frac{-40-4\sqrt{10}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{10}}{2*-24}=\frac{-40+4\sqrt{10}}{-48}
$