14r+15=2r^2

Solution for 14r+15=2r^2 equation:

14r+15=2r^2

We move all terms to the left:

14r+15-(2r^2)=0

determiningTheFunctionDomain
-2r^2+14r+15=0

a = -2; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·(-2)·15
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{79}}{2*-2}=\frac{-14-2\sqrt{79}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{79}}{2*-2}=\frac{-14+2\sqrt{79}}{-4}
$