8-5(4-3x)=2(4-x)8x

Solution for 8-5(4-3x)=2(4-x)8x equation:

8-5(4-3x)=2(4-x)8x

We move all terms to the left:

8-5(4-3x)-(2(4-x)8x)=0

We add all the numbers together, and all the variables

-5(-3x+4)-(2(-1x+4)8x)+8=0

We multiply parentheses

15x-(2(-1x+4)8x)-20+8=0


We calculate terms in parentheses: -(2(-1x+4)8x), so:

2(-1x+4)8x

We multiply parentheses

-16x^2+64x

Back to the equation:

-(-16x^2+64x)


We add all the numbers together, and all the variables

-(-16x^2+64x)+15x-12=0

We get rid of parentheses

16x^2-64x+15x-12=0

We add all the numbers together, and all the variables

16x^2-49x-12=0

a = 16; b = -49; c = -12;
Δ = b2-4ac
Δ = -492-4·16·(-12)
Δ = 3169
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{-(-49)-\sqrt{3169}}{2*16}=\frac{49-\sqrt{3169}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{3169}}{2*16}=\frac{49+\sqrt{3169}}{32}
$