3-9x=7x(x+5)

Solution for 3-9x=7x(x+5) equation:

3-9x=7x(x+5)

We move all terms to the left:

3-9x-(7x(x+5))=0


We calculate terms in parentheses: -(7x(x+5)), so:

7x(x+5)

We multiply parentheses

7x^2+35x

Back to the equation:

-(7x^2+35x)


We get rid of parentheses

-7x^2-9x-35x+3=0

We add all the numbers together, and all the variables

-7x^2-44x+3=0

a = -7; b = -44; c = +3;
Δ = b2-4ac
Δ = -442-4·(-7)·3
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{505}}{2*-7}=\frac{44-2\sqrt{505}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{505}}{2*-7}=\frac{44+2\sqrt{505}}{-14}
$