4x+7(x)^2=2

Solution for 4x+7(x)^2=2 equation:

4x+7(x)^2=2

We move all terms to the left:

4x+7(x)^2-(2)=0

determiningTheFunctionDomain
7x^2+4x-2=0

a = 7; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·7·(-2)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*7}=\frac{-4-6\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*7}=\frac{-4+6\sqrt{2}}{14}
$