-457(x+4)+30=-56x(365+400x)+2

Solution for -457(x+4)+30=-56x(365+400x)+2 equation:

-457(x+4)+30=-56x(365+400x)+2

We move all terms to the left:

-457(x+4)+30-(-56x(365+400x)+2)=0

We add all the numbers together, and all the variables

-457(x+4)-(-56x(400x+365)+2)+30=0

We multiply parentheses

-457x-(-56x(400x+365)+2)-1828+30=0


We calculate terms in parentheses: -(-56x(400x+365)+2), so:

-56x(400x+365)+2

We multiply parentheses

-22400x^2-20440x+2

Back to the equation:

-(-22400x^2-20440x+2)


We add all the numbers together, and all the variables

-(-22400x^2-20440x+2)-457x-1798=0

We get rid of parentheses

22400x^2+20440x-457x-2-1798=0

We add all the numbers together, and all the variables

22400x^2+19983x-1800=0

a = 22400; b = 19983; c = -1800;
Δ = b2-4ac
Δ = 199832-4·22400·(-1800)
Δ = 560600289
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:

$\sqrt{\Delta}=\sqrt{560600289}=\sqrt{9*62288921}=\sqrt{9}*\sqrt{62288921}=3\sqrt{62288921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19983)-3\sqrt{62288921}}{2*22400}=\frac{-19983-3\sqrt{62288921}}{44800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19983)+3\sqrt{62288921}}{2*22400}=\frac{-19983+3\sqrt{62288921}}{44800}
$