170=(4x+1)(x+1)

Solution for 170=(4x+1)(x+1) equation:

170=(4x+1)(x+1)

We move all terms to the left:

170-((4x+1)(x+1))=0

We multiply parentheses ..

-((+4x^2+4x+x+1))+170=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+170=0

We add all the numbers together, and all the variables

-4x^2-5x+169=0

a = -4; b = -5; c = +169;
Δ = b2-4ac
Δ = -52-4·(-4)·169
Δ = 2729
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{-(-5)-\sqrt{2729}}{2*-4}=\frac{5-\sqrt{2729}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2729}}{2*-4}=\frac{5+\sqrt{2729}}{-8}
$