10x-3+4=5+8x(4-3x)

Solution for 10x-3+4=5+8x(4-3x) equation:

10x-3+4=5+8x(4-3x)

We move all terms to the left:

10x-3+4-(5+8x(4-3x))=0

We add all the numbers together, and all the variables

10x-(5+8x(-3x+4))-3+4=0

We add all the numbers together, and all the variables

10x-(5+8x(-3x+4))+1=0


We calculate terms in parentheses: -(5+8x(-3x+4)), so:

5+8x(-3x+4)

determiningTheFunctionDomain
8x(-3x+4)+5

We multiply parentheses

-24x^2+32x+5

Back to the equation:

-(-24x^2+32x+5)


We get rid of parentheses

24x^2-32x+10x-5+1=0

We add all the numbers together, and all the variables

24x^2-22x-4=0

a = 24; b = -22; c = -4;
Δ = b2-4ac
Δ = -222-4·24·(-4)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{217}}{2*24}=\frac{22-2\sqrt{217}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{217}}{2*24}=\frac{22+2\sqrt{217}}{48}
$