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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(x-5)+7x-(5(-1x+3))=0

We add all the numbers together, and all the variables

7x+3x(x-5)-(5(-1x+3))=0

We multiply parentheses

3x^2+7x-15x-(5(-1x+3))=0


We calculate terms in parentheses: -(5(-1x+3)), so:

5(-1x+3)

We multiply parentheses

-5x+15

Back to the equation:

-(-5x+15)


We add all the numbers together, and all the variables

3x^2-8x-(-5x+15)=0

We get rid of parentheses

3x^2-8x+5x-15=0

We add all the numbers together, and all the variables

3x^2-3x-15=0

a = 3; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·3·(-15)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*3}=\frac{3-3\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*3}=\frac{3+3\sqrt{21}}{6}
$