r2-14r+30=0

Solution for r2-14r+30=0 equation:

r2-14r+30=0

We add all the numbers together, and all the variables

r^2-14r+30=0

a = 1; b = -14; c = +30;
Δ = b2-4ac
Δ = -142-4·1·30
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{19}}{2*1}=\frac{14-2\sqrt{19}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*1}=\frac{14+2\sqrt{19}}{2}
$