(7x-1)(2x+9)=79

Solution for (7x-1)(2x+9)=79 equation:

(7x-1)(2x+9)=79

We move all terms to the left:

(7x-1)(2x+9)-(79)=0

We multiply parentheses ..

(+14x^2+63x-2x-9)-79=0

We get rid of parentheses

14x^2+63x-2x-9-79=0

We add all the numbers together, and all the variables

14x^2+61x-88=0

a = 14; b = 61; c = -88;
Δ = b2-4ac
Δ = 612-4·14·(-88)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-93}{2*14}=\frac{-154}{28}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+93}{2*14}=\frac{32}{28}
=1+1/7
$