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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4(x-15)

We multiply parentheses

4x-60

Back to the equation:

-(4x-60)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-9x^2+14x+60=0

a = -9; b = 14; c = +60;
Δ = b2-4ac
Δ = 142-4·(-9)·60
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{589}}{2*-9}=\frac{-14-2\sqrt{589}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{589}}{2*-9}=\frac{-14+2\sqrt{589}}{-18}
$