2a^2+14a-27=0

Solution for 2a^2+14a-27=0 equation:

2a^2+14a-27=0

a = 2; b = 14; c = -27;
Δ = b2-4ac
Δ = 142-4·2·(-27)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{103}}{2*2}=\frac{-14-2\sqrt{103}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{103}}{2*2}=\frac{-14+2\sqrt{103}}{4}
$