r2-15=r+19

Solution for r2-15=r+19 equation:

r2-15=r+19

We move all terms to the left:

r2-15-(r+19)=0

We add all the numbers together, and all the variables

r^2-(r+19)-15=0

We get rid of parentheses

r^2-r-19-15=0

We add all the numbers together, and all the variables

r^2-1r-34=0

a = 1; b = -1; c = -34;
Δ = b2-4ac
Δ = -12-4·1·(-34)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{137}}{2*1}=\frac{1-\sqrt{137}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{137}}{2*1}=\frac{1+\sqrt{137}}{2}
$