7x(2x-3)=8x+39

Solution for 7x(2x-3)=8x+39 equation:

7x(2x-3)=8x+39

We move all terms to the left:

7x(2x-3)-(8x+39)=0

We multiply parentheses

14x^2-21x-(8x+39)=0

We get rid of parentheses

14x^2-21x-8x-39=0

We add all the numbers together, and all the variables

14x^2-29x-39=0

a = 14; b = -29; c = -39;
Δ = b2-4ac
Δ = -292-4·14·(-39)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-55}{2*14}=\frac{-26}{28}
=-13/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+55}{2*14}=\frac{84}{28}
=3
$