3x+5=8x(6-5x)

Solution for 3x+5=8x(6-5x) equation:

3x+5=8x(6-5x)

We move all terms to the left:

3x+5-(8x(6-5x))=0

We add all the numbers together, and all the variables

3x-(8x(-5x+6))+5=0


We calculate terms in parentheses: -(8x(-5x+6)), so:

8x(-5x+6)

We multiply parentheses

-40x^2+48x

Back to the equation:

-(-40x^2+48x)


We get rid of parentheses

40x^2-48x+3x+5=0

We add all the numbers together, and all the variables

40x^2-45x+5=0

a = 40; b = -45; c = +5;
Δ = b2-4ac
Δ = -452-4·40·5
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-35}{2*40}=\frac{10}{80}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+35}{2*40}=\frac{80}{80}
=1
$