10-2x=14x2

Solution for 10-2x=14x2 equation:

10-2x=14x^2

We move all terms to the left:

10-2x-(14x^2)=0

determiningTheFunctionDomain
-14x^2-2x+10=0

a = -14; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-14)·10
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{141}}{2*-14}=\frac{2-2\sqrt{141}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{141}}{2*-14}=\frac{2+2\sqrt{141}}{-28}
$