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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(8x-5x(x-5))+9+8=0


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

8x-5x(x-5)

We multiply parentheses

-5x^2+8x+25x

We add all the numbers together, and all the variables

-5x^2+33x

Back to the equation:

-(-5x^2+33x)


We add all the numbers together, and all the variables

-(-5x^2+33x)+3x+17=0

We get rid of parentheses

5x^2-33x+3x+17=0

We add all the numbers together, and all the variables

5x^2-30x+17=0

a = 5; b = -30; c = +17;
Δ = b2-4ac
Δ = -302-4·5·17
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{35}}{2*5}=\frac{30-4\sqrt{35}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{35}}{2*5}=\frac{30+4\sqrt{35}}{10}
$