7x^2-6=-41x

Solution for 7x^2-6=-41x equation:

7x^2-6=-41x

We move all terms to the left:

7x^2-6-(-41x)=0

We get rid of parentheses

7x^2+41x-6=0

a = 7; b = 41; c = -6;
Δ = b2-4ac
Δ = 412-4·7·(-6)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-43}{2*7}=\frac{-84}{14}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+43}{2*7}=\frac{2}{14}
=1/7
$