5r^2-14r-45=0

Solution for 5r^2-14r-45=0 equation:

5r^2-14r-45=0

a = 5; b = -14; c = -45;
Δ = b2-4ac
Δ = -142-4·5·(-45)
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{274}}{2*5}=\frac{14-2\sqrt{274}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{274}}{2*5}=\frac{14+2\sqrt{274}}{10}
$