5x2+41x+40=-2

Solution for 5x2+41x+40=-2 equation:

5x^2+41x+40=-2

We move all terms to the left:

5x^2+41x+40-(-2)=0

We add all the numbers together, and all the variables

5x^2+41x+42=0

a = 5; b = 41; c = +42;
Δ = b2-4ac
Δ = 412-4·5·42
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*5}=\frac{-12}{10}
=-1+1/5
$