x+7=2x2

Solution for x+7=2x2 equation:

x+7=2x^2

We move all terms to the left:

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

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

a = -2; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-2)·7
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{57}}{2*-2}=\frac{-1-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-2}=\frac{-1+\sqrt{57}}{-4}
$