49a^2+301a=-42

Solution for 49a^2+301a=-42 equation:

49a^2+301a=-42

We move all terms to the left:

49a^2+301a-(-42)=0

We add all the numbers together, and all the variables

49a^2+301a+42=0

a = 49; b = 301; c = +42;
Δ = b2-4ac
Δ = 3012-4·49·42
Δ = 82369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82369}=287$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(301)-287}{2*49}=\frac{-588}{98}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(301)+287}{2*49}=\frac{-14}{98}
=-1/7
$