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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

6x-(5(x+3)5x)-15=0


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

5(x+3)5x

We multiply parentheses

25x^2+75x

Back to the equation:

-(25x^2+75x)


We get rid of parentheses

-25x^2+6x-75x-15=0

We add all the numbers together, and all the variables

-25x^2-69x-15=0

a = -25; b = -69; c = -15;
Δ = b2-4ac
Δ = -692-4·(-25)·(-15)
Δ = 3261
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{-(-69)-\sqrt{3261}}{2*-25}=\frac{69-\sqrt{3261}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{3261}}{2*-25}=\frac{69+\sqrt{3261}}{-50}
$