18a^2+76a=3

Solution for 18a^2+76a=3 equation:

18a^2+76a=3

We move all terms to the left:

18a^2+76a-(3)=0

a = 18; b = 76; c = -3;
Δ = b2-4ac
Δ = 762-4·18·(-3)
Δ = 5992
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:

$\sqrt{\Delta}=\sqrt{5992}=\sqrt{4*1498}=\sqrt{4}*\sqrt{1498}=2\sqrt{1498}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{1498}}{2*18}=\frac{-76-2\sqrt{1498}}{36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{1498}}{2*18}=\frac{-76+2\sqrt{1498}}{36}
$