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-2x^{2}+5x+6=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{-5±\sqrt{5^{2}-4\left(-2\right)\times 6}}{2\left(-2\right)}
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{-5±\sqrt{25-4\left(-2\right)\times 6}}{2\left(-2\right)}
5 kvadratini chiqarish.
x=\frac{-5±\sqrt{25+8\times 6}}{2\left(-2\right)}
-4 ni -2 marotabaga ko'paytirish.
x=\frac{-5±\sqrt{25+48}}{2\left(-2\right)}
8 ni 6 marotabaga ko'paytirish.
x=\frac{-5±\sqrt{73}}{2\left(-2\right)}
25 ni 48 ga qo'shish.
x=\frac{-5±\sqrt{73}}{-4}
2 ni -2 marotabaga ko'paytirish.
x=\frac{\sqrt{73}-5}{-4}
x=\frac{-5±\sqrt{73}}{-4} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{73} ga qo'shish.
x=\frac{5-\sqrt{73}}{4}
-5+\sqrt{73} ni -4 ga bo'lish.
x=\frac{-\sqrt{73}-5}{-4}
x=\frac{-5±\sqrt{73}}{-4} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{73} ni ayirish.
x=\frac{\sqrt{73}+5}{4}
-5-\sqrt{73} ni -4 ga bo'lish.
-2x^{2}+5x+6=-2\left(x-\frac{5-\sqrt{73}}{4}\right)\left(x-\frac{\sqrt{73}+5}{4}\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5-\sqrt{73}}{4} ga va x_{2} uchun \frac{5+\sqrt{73}}{4} ga bo‘ling.