7x(x-3)=5(x+3)

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

7x(x-3)=5(x+3)

We move all terms to the left:

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

We multiply parentheses

7x^2-21x-(5(x+3))=0


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

5(x+3)

We multiply parentheses

5x+15

Back to the equation:

-(5x+15)


We get rid of parentheses

7x^2-21x-5x-15=0

We add all the numbers together, and all the variables

7x^2-26x-15=0

a = 7; b = -26; c = -15;
Δ = b2-4ac
Δ = -262-4·7·(-15)
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{274}}{2*7}=\frac{26-2\sqrt{274}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{274}}{2*7}=\frac{26+2\sqrt{274}}{14}
$