-16x+433(x-1)=-3x(-15x-3)+3=

Solution for -16x+433(x-1)=-3x(-15x-3)+3= equation:

-16x+433(x-1)=-3x(-15x-3)+3=

We move all terms to the left:

-16x+433(x-1)-(-3x(-15x-3)+3)=0

We multiply parentheses

-16x+433x-(-3x(-15x-3)+3)-433=0


We calculate terms in parentheses: -(-3x(-15x-3)+3), so:

-3x(-15x-3)+3

We multiply parentheses

45x^2+9x+3

Back to the equation:

-(45x^2+9x+3)


We add all the numbers together, and all the variables

417x-(45x^2+9x+3)-433=0

We get rid of parentheses

-45x^2+417x-9x-3-433=0

We add all the numbers together, and all the variables

-45x^2+408x-436=0

a = -45; b = 408; c = -436;
Δ = b2-4ac
Δ = 4082-4·(-45)·(-436)
Δ = 87984
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:

$\sqrt{\Delta}=\sqrt{87984}=\sqrt{144*611}=\sqrt{144}*\sqrt{611}=12\sqrt{611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(408)-12\sqrt{611}}{2*-45}=\frac{-408-12\sqrt{611}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(408)+12\sqrt{611}}{2*-45}=\frac{-408+12\sqrt{611}}{-90}
$