7x^2+35x=-42

Solution for 7x^2+35x=-42 equation:

7x^2+35x=-42

We move all terms to the left:

7x^2+35x-(-42)=0

We add all the numbers together, and all the variables

7x^2+35x+42=0

a = 7; b = 35; c = +42;
Δ = b2-4ac
Δ = 352-4·7·42
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7}{2*7}=\frac{-42}{14}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7}{2*7}=\frac{-28}{14}
=-2
$