3x+14=2x^2

Solution for 3x+14=2x^2 equation:

3x+14=2x^2

We move all terms to the left:

3x+14-(2x^2)=0

determiningTheFunctionDomain
-2x^2+3x+14=0

a = -2; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-2)·14
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-11}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*-2}=\frac{8}{-4}
=-2
$