5r^2-7r+8=r^2+16r+14

Solution for 5r^2-7r+8=r^2+16r+14 equation:

5r^2-7r+8=r^2+16r+14

We move all terms to the left:

5r^2-7r+8-(r^2+16r+14)=0

We get rid of parentheses

5r^2-r^2-7r-16r-14+8=0

We add all the numbers together, and all the variables

4r^2-23r-6=0

a = 4; b = -23; c = -6;
Δ = b2-4ac
Δ = -232-4·4·(-6)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*4}=\frac{-2}{8}
=-1/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*4}=\frac{48}{8}
=6
$