7x^2+5x-17=31-29x

Solution for 7x^2+5x-17=31-29x equation:

7x^2+5x-17=31-29x

We move all terms to the left:

7x^2+5x-17-(31-29x)=0

We add all the numbers together, and all the variables

7x^2+5x-(-29x+31)-17=0

We get rid of parentheses

7x^2+5x+29x-31-17=0

We add all the numbers together, and all the variables

7x^2+34x-48=0

a = 7; b = 34; c = -48;
Δ = b2-4ac
Δ = 342-4·7·(-48)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-50}{2*7}=\frac{-84}{14}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+50}{2*7}=\frac{16}{14}
=1+1/7
$