10x^2-41x=-42

Solution for 10x^2-41x=-42 equation:

10x^2-41x=-42

We move all terms to the left:

10x^2-41x-(-42)=0

We add all the numbers together, and all the variables

10x^2-41x+42=0

a = 10; b = -41; c = +42;
Δ = b2-4ac
Δ = -412-4·10·42
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-1}{2*10}=\frac{40}{20}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+1}{2*10}=\frac{42}{20}
=2+1/10
$