14r2=5-7r

Solution for 14r2=5-7r equation:

14r^2=5-7r

We move all terms to the left:

14r^2-(5-7r)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

14r^2+7r-5=0

a = 14; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·14·(-5)
Δ = 329
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{-(7)-\sqrt{329}}{2*14}=\frac{-7-\sqrt{329}}{28}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{329}}{2*14}=\frac{-7+\sqrt{329}}{28}
$