-9x(x-2)=4x(x-15)

Solution for -9x(x-2)=4x(x-15) equation:

-9x(x-2)=4x(x-15)

We move all terms to the left:

-9x(x-2)-(4x(x-15))=0

We multiply parentheses

-9x^2+18x-(4x(x-15))=0


We calculate terms in parentheses: -(4x(x-15)), so:

4x(x-15)

We multiply parentheses

4x^2-60x

Back to the equation:

-(4x^2-60x)


We get rid of parentheses

-9x^2-4x^2+18x+60x=0

We add all the numbers together, and all the variables

-13x^2+78x=0

a = -13; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·(-13)·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*-13}=\frac{-156}{-26}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*-13}=\frac{0}{-26}
=0
$