-4a^2+14a+18=0

Solution for -4a^2+14a+18=0 equation:

-4a^2+14a+18=0

a = -4; b = 14; c = +18;
Δ = b2-4ac
Δ = 142-4·(-4)·18
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*-4}=\frac{-36}{-8}
=4+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*-4}=\frac{8}{-8}
=-1
$