9x=2x(x+35)

Solution for 9x=2x(x+35) equation:

9x=2x(x+35)

We move all terms to the left:

9x-(2x(x+35))=0


We calculate terms in parentheses: -(2x(x+35)), so:

2x(x+35)

We multiply parentheses

2x^2+70x

Back to the equation:

-(2x^2+70x)


We get rid of parentheses

-2x^2+9x-70x=0

We add all the numbers together, and all the variables

-2x^2-61x=0

a = -2; b = -61; c = 0;
Δ = b2-4ac
Δ = -612-4·(-2)·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-61}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+61}{2*-2}=\frac{122}{-4}
=-30+1/2
$