8x=(3x+5)(6x-16)

Solution for 8x=(3x+5)(6x-16) equation:

8x=(3x+5)(6x-16)

We move all terms to the left:

8x-((3x+5)(6x-16))=0

We multiply parentheses ..

-((+18x^2-48x+30x-80))+8x=0


We calculate terms in parentheses: -((+18x^2-48x+30x-80)), so:

(+18x^2-48x+30x-80)

We get rid of parentheses

18x^2-48x+30x-80

We add all the numbers together, and all the variables

18x^2-18x-80

Back to the equation:

-(18x^2-18x-80)


We add all the numbers together, and all the variables

8x-(18x^2-18x-80)=0

We get rid of parentheses

-18x^2+8x+18x+80=0

We add all the numbers together, and all the variables

-18x^2+26x+80=0

a = -18; b = 26; c = +80;
Δ = b2-4ac
Δ = 262-4·(-18)·80
Δ = 6436
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:

$\sqrt{\Delta}=\sqrt{6436}=\sqrt{4*1609}=\sqrt{4}*\sqrt{1609}=2\sqrt{1609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1609}}{2*-18}=\frac{-26-2\sqrt{1609}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1609}}{2*-18}=\frac{-26+2\sqrt{1609}}{-36}
$