5x^2-41x-46=10

Solution for 5x^2-41x-46=10 equation:

5x^2-41x-46=10

We move all terms to the left:

5x^2-41x-46-(10)=0

We add all the numbers together, and all the variables

5x^2-41x-56=0

a = 5; b = -41; c = -56;
Δ = b2-4ac
Δ = -412-4·5·(-56)
Δ = 2801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{2801}}{2*5}=\frac{41-\sqrt{2801}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{2801}}{2*5}=\frac{41+\sqrt{2801}}{10}
$