-15x(3x-31)=2(x-3)-9

Solution for -15x(3x-31)=2(x-3)-9 equation:

-15x(3x-31)=2(x-3)-9

We move all terms to the left:

-15x(3x-31)-(2(x-3)-9)=0

We multiply parentheses

-45x^2+465x-(2(x-3)-9)=0


We calculate terms in parentheses: -(2(x-3)-9), so:

2(x-3)-9

We multiply parentheses

2x-6-9

We add all the numbers together, and all the variables

2x-15

Back to the equation:

-(2x-15)


We get rid of parentheses

-45x^2+465x-2x+15=0

We add all the numbers together, and all the variables

-45x^2+463x+15=0

a = -45; b = 463; c = +15;
Δ = b2-4ac
Δ = 4632-4·(-45)·15
Δ = 217069
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(463)-\sqrt{217069}}{2*-45}=\frac{-463-\sqrt{217069}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(463)+\sqrt{217069}}{2*-45}=\frac{-463+\sqrt{217069}}{-90}
$