Whakaoti i te {l}{4ac-b^2/4a=x}{a=-3/2}{b=1/2}{c=9/2}

$$\left\{ \begin{array} { l } { \frac { 4 a c - b ^ { 2 } } { 4 a } = x } \\ { a = - \frac { 3 } { 2 } } \\ { b = \frac { 1 } { 2 } } \\ { c = \frac { 9 } { 2 } } \end{array} \right.$$

Whakaoti mō a, c, b, x

$$x = \frac{109}{24} = 4\frac{13}{24} \approx 4.541666667$$

$$a = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$c = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$b=\frac{1}{2}=0.5$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$\frac{4\left(-\frac{3}{2}\right)\times \frac{9}{2}-\left(\frac{1}{2}\right)^{2}}{4\left(-\frac{3}{2}\right)}=x$$

Whakareatia te 4 ki te -\frac{3}{2}, ka -6.

$$\frac{-6\times \frac{9}{2}-\left(\frac{1}{2}\right)^{2}}{4\left(-\frac{3}{2}\right)}=x$$

Whakareatia te -6 ki te \frac{9}{2}, ka -27.

$$\frac{-27-\left(\frac{1}{2}\right)^{2}}{4\left(-\frac{3}{2}\right)}=x$$

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

$$\frac{-27-\frac{1}{4}}{4\left(-\frac{3}{2}\right)}=x$$

Tangohia te \frac{1}{4} i te -27, ka -\frac{109}{4}.

$$\frac{-\frac{109}{4}}{4\left(-\frac{3}{2}\right)}=x$$

Whakareatia te 4 ki te -\frac{3}{2}, ka -6.

$$\frac{-\frac{109}{4}}{-6}=x$$

Tuhia te \frac{-\frac{109}{4}}{-6} hei hautanga kotahi.

$$\frac{-109}{4\left(-6\right)}=x$$

Whakareatia te 4 ki te -6, ka -24.

$$\frac{-109}{-24}=x$$

Ka taea te hautanga \frac{-109}{-24} te whakamāmā ki te \frac{109}{24} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$\frac{109}{24}=x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x=\frac{109}{24}$$

Kua oti te pūnaha te whakatau.

$$a=-\frac{3}{2} c=\frac{9}{2} b=\frac{1}{2} x=\frac{109}{24}$$