10x^2+2x-46=x-4

Solution for 10x^2+2x-46=x-4 equation:

10x^2+2x-46=x-4

We move all terms to the left:

10x^2+2x-46-(x-4)=0

We get rid of parentheses

10x^2+2x-x+4-46=0

We add all the numbers together, and all the variables

10x^2+x-42=0

a = 10; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·10·(-42)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*10}=\frac{-42}{20}
=-2+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*10}=\frac{40}{20}
=2
$