3x+8=2x2

Solution for 3x+8=2x2 equation:

3x+8=2x^2

We move all terms to the left:

3x+8-(2x^2)=0

determiningTheFunctionDomain
-2x^2+3x+8=0

a = -2; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-2)·8
Δ = 73
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{-(3)-\sqrt{73}}{2*-2}=\frac{-3-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{73}}{2*-2}=\frac{-3+\sqrt{73}}{-4}
$