```Question 200756

Notice that the quadratic {{{2h^2-h-3}}} is in the form of {{{Ah^2+Bh+C}}} where {{{A=2}}}, {{{B=-1}}}, and {{{C=-3}}}

Let's use the quadratic formula to solve for "h":

{{{h = (-(-1) +- sqrt( (-1)^2-4(2)(-3) ))/(2(2))}}} Plug in  {{{A=2}}}, {{{B=-1}}}, and {{{C=-3}}}

{{{h = (1 +- sqrt( (-1)^2-4(2)(-3) ))/(2(2))}}} Negate {{{-1}}} to get {{{1}}}.

{{{h = (1 +- sqrt( 1-4(2)(-3) ))/(2(2))}}} Square {{{-1}}} to get {{{1}}}.

{{{h = (1 +- sqrt( 1--24 ))/(2(2))}}} Multiply {{{4(2)(-3)}}} to get {{{-24}}}

{{{h = (1 +- sqrt( 1+24 ))/(2(2))}}} Rewrite {{{sqrt(1--24)}}} as {{{sqrt(1+24)}}}

{{{h = (1 +- sqrt( 25 ))/(2(2))}}} Add {{{1}}} to {{{24}}} to get {{{25}}}

{{{h = (1 +- sqrt( 25 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}.

{{{h = (1 +- 5)/(4)}}} Take the square root of {{{25}}} to get {{{5}}}.

{{{h = (1 + 5)/(4)}}} or {{{h = (1 - 5)/(4)}}} Break up the expression.

{{{h = (6)/(4)}}} or {{{h =  (-4)/(4)}}} Combine like terms.

{{{h = 3/2}}} or {{{h = -1}}} Simplify.

So the solutions are {{{h = 3/2}}} or {{{h = -1}}}

```