7a^2+4a=147

Solution for 7a^2+4a=147 equation:

7a^2+4a=147

We move all terms to the left:

7a^2+4a-(147)=0

a = 7; b = 4; c = -147;
Δ = b2-4ac
Δ = 42-4·7·(-147)
Δ = 4132
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:

$\sqrt{\Delta}=\sqrt{4132}=\sqrt{4*1033}=\sqrt{4}*\sqrt{1033}=2\sqrt{1033}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{1033}}{2*7}=\frac{-4-2\sqrt{1033}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{1033}}{2*7}=\frac{-4+2\sqrt{1033}}{14}
$