9(x-7)=-3x(x+53)

Solution for 9(x-7)=-3x(x+53) equation:

9(x-7)=-3x(x+53)

We move all terms to the left:

9(x-7)-(-3x(x+53))=0

We multiply parentheses

9x-(-3x(x+53))-63=0


We calculate terms in parentheses: -(-3x(x+53)), so:

-3x(x+53)

We multiply parentheses

-3x^2-159x

Back to the equation:

-(-3x^2-159x)


We get rid of parentheses

3x^2+159x+9x-63=0

We add all the numbers together, and all the variables

3x^2+168x-63=0

a = 3; b = 168; c = -63;
Δ = b2-4ac
Δ = 1682-4·3·(-63)
Δ = 28980
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:

$\sqrt{\Delta}=\sqrt{28980}=\sqrt{36*805}=\sqrt{36}*\sqrt{805}=6\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-6\sqrt{805}}{2*3}=\frac{-168-6\sqrt{805}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+6\sqrt{805}}{2*3}=\frac{-168+6\sqrt{805}}{6}
$