7x^2+3x-17=39-38x

Solution for 7x^2+3x-17=39-38x equation:

7x^2+3x-17=39-38x

We move all terms to the left:

7x^2+3x-17-(39-38x)=0

We add all the numbers together, and all the variables

7x^2+3x-(-38x+39)-17=0

We get rid of parentheses

7x^2+3x+38x-39-17=0

We add all the numbers together, and all the variables

7x^2+41x-56=0

a = 7; b = 41; c = -56;
Δ = b2-4ac
Δ = 412-4·7·(-56)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-57}{2*7}=\frac{-98}{14}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+57}{2*7}=\frac{16}{14}
=1+1/7
$