-4(x+8)+23x(x=2)

Solution for -4(x+8)+23x(x=2) equation:

-4(x+8)+23x(x=2)

We move all terms to the left:

-4(x+8)+23x(x-(2))=0

We multiply parentheses

23x^2-4x-46x-32=0

We add all the numbers together, and all the variables

23x^2-50x-32=0

a = 23; b = -50; c = -32;
Δ = b2-4ac
Δ = -502-4·23·(-32)
Δ = 5444
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:

$\sqrt{\Delta}=\sqrt{5444}=\sqrt{4*1361}=\sqrt{4}*\sqrt{1361}=2\sqrt{1361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1361}}{2*23}=\frac{50-2\sqrt{1361}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1361}}{2*23}=\frac{50+2\sqrt{1361}}{46}
$