(3x-7)(5+2x)=5

Solution for (3x-7)(5+2x)=5 equation:

(3x-7)(5+2x)=5

We move all terms to the left:

(3x-7)(5+2x)-(5)=0

We add all the numbers together, and all the variables

(3x-7)(2x+5)-5=0

We multiply parentheses ..

(+6x^2+15x-14x-35)-5=0

We get rid of parentheses

6x^2+15x-14x-35-5=0

We add all the numbers together, and all the variables

6x^2+x-40=0

a = 6; b = 1; c = -40;
Δ = b2-4ac
Δ = 12-4·6·(-40)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*6}=\frac{30}{12}
=2+1/2
$