10x^2+2x=46

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

10x^2+2x=46

We move all terms to the left:

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

a = 10; b = 2; c = -46;
Δ = b2-4ac
Δ = 22-4·10·(-46)
Δ = 1844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1844}=\sqrt{4*461}=\sqrt{4}*\sqrt{461}=2\sqrt{461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{461}}{2*10}=\frac{-2-2\sqrt{461}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{461}}{2*10}=\frac{-2+2\sqrt{461}}{20}
$