9a^2+42a=49

Solution for 9a^2+42a=49 equation:

9a^2+42a=49

We move all terms to the left:

9a^2+42a-(49)=0

a = 9; b = 42; c = -49;
Δ = b2-4ac
Δ = 422-4·9·(-49)
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42\sqrt{2}}{2*9}=\frac{-42-42\sqrt{2}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42\sqrt{2}}{2*9}=\frac{-42+42\sqrt{2}}{18}
$