7x^2+3x-17=55-52x

Solution for 7x^2+3x-17=55-52x equation:

7x^2+3x-17=55-52x

We move all terms to the left:

7x^2+3x-17-(55-52x)=0

We add all the numbers together, and all the variables

7x^2+3x-(-52x+55)-17=0

We get rid of parentheses

7x^2+3x+52x-55-17=0

We add all the numbers together, and all the variables

7x^2+55x-72=0

a = 7; b = 55; c = -72;
Δ = b2-4ac
Δ = 552-4·7·(-72)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-71}{2*7}=\frac{-126}{14}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+71}{2*7}=\frac{16}{14}
=1+1/7
$