2x^2=16-3x

Solution for 2x^2=16-3x equation:

2x^2=16-3x

We move all terms to the left:

2x^2-(16-3x)=0

We add all the numbers together, and all the variables

2x^2-(-3x+16)=0

We get rid of parentheses

2x^2+3x-16=0

a = 2; b = 3; c = -16;
Δ = b2-4ac
Δ = 32-4·2·(-16)
Δ = 137
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{137}}{2*2}=\frac{-3-\sqrt{137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{137}}{2*2}=\frac{-3+\sqrt{137}}{4}
$