7r2=14+8r

Solution for 7r2=14+8r equation:

7r^2=14+8r

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

7r^2-8r-14=0

a = 7; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·7·(-14)
Δ = 456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{114}}{2*7}=\frac{8-2\sqrt{114}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{114}}{2*7}=\frac{8+2\sqrt{114}}{14}
$