(7x+1)(2x-3)=52

Solution for (7x+1)(2x-3)=52 equation:

(7x+1)(2x-3)=52

We move all terms to the left:

(7x+1)(2x-3)-(52)=0

We multiply parentheses ..

(+14x^2-21x+2x-3)-52=0

We get rid of parentheses

14x^2-21x+2x-3-52=0

We add all the numbers together, and all the variables

14x^2-19x-55=0

a = 14; b = -19; c = -55;
Δ = b2-4ac
Δ = -192-4·14·(-55)
Δ = 3441
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{-(-19)-\sqrt{3441}}{2*14}=\frac{19-\sqrt{3441}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{3441}}{2*14}=\frac{19+\sqrt{3441}}{28}
$