7x^2+41x=-2x+42

Solution for 7x^2+41x=-2x+42 equation:

7x^2+41x=-2x+42

We move all terms to the left:

7x^2+41x-(-2x+42)=0

We get rid of parentheses

7x^2+41x+2x-42=0

We add all the numbers together, and all the variables

7x^2+43x-42=0

a = 7; b = 43; c = -42;
Δ = b2-4ac
Δ = 432-4·7·(-42)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-55}{2*7}=\frac{-98}{14}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+55}{2*7}=\frac{12}{14}
=6/7
$