(X+7)(2x+1)=57

Solution for (X+7)(2x+1)=57 equation:

(X+7)(2X+1)=57

We move all terms to the left:

(X+7)(2X+1)-(57)=0

We multiply parentheses ..

(+2X^2+X+14X+7)-57=0

We get rid of parentheses

2X^2+X+14X+7-57=0

We add all the numbers together, and all the variables

2X^2+15X-50=0

a = 2; b = 15; c = -50;
Δ = b2-4ac
Δ = 152-4·2·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*2}=\frac{-40}{4}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*2}=\frac{10}{4}
=2+1/2
$