81=(x-7)2x+x

Solution for 81=(x-7)2x+x equation:

81=(x-7)2x+x

We move all terms to the left:

81-((x-7)2x+x)=0


We calculate terms in parentheses: -((x-7)2x+x), so:

(x-7)2x+x

We add all the numbers together, and all the variables

x+(x-7)2x

We multiply parentheses

2x^2+x-14x

We add all the numbers together, and all the variables

2x^2-13x

Back to the equation:

-(2x^2-13x)


We get rid of parentheses

-2x^2+13x+81=0

a = -2; b = 13; c = +81;
Δ = b2-4ac
Δ = 132-4·(-2)·81
Δ = 817
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{-(13)-\sqrt{817}}{2*-2}=\frac{-13-\sqrt{817}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{817}}{2*-2}=\frac{-13+\sqrt{817}}{-4}
$