(2x+1)(x-7)=8x

Solution for (2x+1)(x-7)=8x equation:

(2x+1)(x-7)=8x

We move all terms to the left:

(2x+1)(x-7)-(8x)=0

We add all the numbers together, and all the variables

-8x+(2x+1)(x-7)=0

We multiply parentheses ..

(+2x^2-14x+x-7)-8x=0

We get rid of parentheses

2x^2-14x+x-8x-7=0

We add all the numbers together, and all the variables

2x^2-21x-7=0

a = 2; b = -21; c = -7;
Δ = b2-4ac
Δ = -212-4·2·(-7)
Δ = 497
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{-(-21)-\sqrt{497}}{2*2}=\frac{21-\sqrt{497}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{497}}{2*2}=\frac{21+\sqrt{497}}{4}
$