15x-31=1(x+8)14x-39

Solution for 15x-31=1(x+8)14x-39 equation:

15x-31=1(x+8)14x-39

We move all terms to the left:

15x-31-(1(x+8)14x-39)=0


We calculate terms in parentheses: -(1(x+8)14x-39), so:

1(x+8)14x-39

We multiply parentheses

14x^2+112x-39

Back to the equation:

-(14x^2+112x-39)


We get rid of parentheses

-14x^2+15x-112x+39-31=0

We add all the numbers together, and all the variables

-14x^2-97x+8=0

a = -14; b = -97; c = +8;
Δ = b2-4ac
Δ = -972-4·(-14)·8
Δ = 9857
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{-(-97)-\sqrt{9857}}{2*-14}=\frac{97-\sqrt{9857}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+\sqrt{9857}}{2*-14}=\frac{97+\sqrt{9857}}{-28}
$