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x^{2}+3x-2=0
Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.
x=\frac{-3±\sqrt{3^{2}-4\left(-2\right)}}{2}
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.
x=\frac{-3±\sqrt{9-4\left(-2\right)}}{2}
3 kvadratini chiqarish.
x=\frac{-3±\sqrt{9+8}}{2}
-4 ni -2 marotabaga ko'paytirish.
x=\frac{-3±\sqrt{17}}{2}
9 ni 8 ga qo'shish.
x=\frac{\sqrt{17}-3}{2}
x=\frac{-3±\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{17} ga qo'shish.
x=\frac{-\sqrt{17}-3}{2}
x=\frac{-3±\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{17} ni ayirish.
x^{2}+3x-2=\left(x-\frac{\sqrt{17}-3}{2}\right)\left(x-\frac{-\sqrt{17}-3}{2}\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3+\sqrt{17}}{2} ga va x_{2} uchun \frac{-3-\sqrt{17}}{2} ga bo‘ling.