15x+7=x^2+31x+35

Solution for 15x+7=x^2+31x+35 equation:

15x+7=x^2+31x+35

We move all terms to the left:

15x+7-(x^2+31x+35)=0

We get rid of parentheses

-x^2+15x-31x-35+7=0

We add all the numbers together, and all the variables

-1x^2-16x-28=0

a = -1; b = -16; c = -28;
Δ = b2-4ac
Δ = -162-4·(-1)·(-28)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*-1}=\frac{28}{-2}
=-14
$