85=(4x+1)*(x+1)

Solution for 85=(4x+1)*(x+1) equation:

85=(4x+1)(x+1)

We move all terms to the left:

85-((4x+1)(x+1))=0

We multiply parentheses ..

-((+4x^2+4x+x+1))+85=0


We calculate terms in parentheses: -((+4x^2+4x+x+1)), so:

(+4x^2+4x+x+1)

We get rid of parentheses

4x^2+4x+x+1

We add all the numbers together, and all the variables

4x^2+5x+1

Back to the equation:

-(4x^2+5x+1)


We get rid of parentheses

-4x^2-5x-1+85=0

We add all the numbers together, and all the variables

-4x^2-5x+84=0

a = -4; b = -5; c = +84;
Δ = b2-4ac
Δ = -52-4·(-4)·84
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-37}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+37}{2*-4}=\frac{42}{-8}
=-5+1/4
$