-7x(x+9)=9(x-5)-14x

Solution for -7x(x+9)=9(x-5)-14x equation:

-7x(x+9)=9(x-5)-14x

We move all terms to the left:

-7x(x+9)-(9(x-5)-14x)=0

We multiply parentheses

-7x^2-63x-(9(x-5)-14x)=0


We calculate terms in parentheses: -(9(x-5)-14x), so:

9(x-5)-14x

We add all the numbers together, and all the variables

-14x+9(x-5)

We multiply parentheses

-14x+9x-45

We add all the numbers together, and all the variables

-5x-45

Back to the equation:

-(-5x-45)


We get rid of parentheses

-7x^2-63x+5x+45=0

We add all the numbers together, and all the variables

-7x^2-58x+45=0

a = -7; b = -58; c = +45;
Δ = b2-4ac
Δ = -582-4·(-7)·45
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-68}{2*-7}=\frac{-10}{-14}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+68}{2*-7}=\frac{126}{-14}
=-9
$