2a^2+14a-25=0

Solution for 2a^2+14a-25=0 equation:

2a^2+14a-25=0

a = 2; b = 14; c = -25;
Δ = b2-4ac
Δ = 142-4·2·(-25)
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{11}}{2*2}=\frac{-14-6\sqrt{11}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{11}}{2*2}=\frac{-14+6\sqrt{11}}{4}
$