2x^{2} +3x-6=0 find roots
Answers
Answer:
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2
2
+
3
−
6
=
0
2x^{2}+3x-6=0
2x2+3x−6=0
Quadratic formula
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
2
+
3
−
6
=
0
2x^{2}+3x-6=0
2x2+3x−6=0
=
2
a={\color{#c92786}{2}}
a=2
=
3
b={\color{#e8710a}{3}}
b=3
=
−
6
c={\color{#129eaf}{-6}}
c=−6
=
−
3
±
3
2
−
4
⋅
2
(
−
6
)
√
2
⋅
2
x=\frac{-{\color{#e8710a}{3}} \pm \sqrt{{\color{#e8710a}{3}}^{2}-4 \cdot {\color{#c92786}{2}}({\color{#129eaf}{-6}})}}{2 \cdot {\color{#c92786}{2}}}
x=2⋅2−3±32−4⋅2(−6)
2
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Multiply the numbers
=
−
3
±
5
7
√
4
x=\frac{-3 \pm \sqrt{57}}{4}
x=4−3±57
3
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
−
3
+
5
7
√
4
x=\frac{-3+\sqrt{57}}{4}
x=4−3+57
=
−
3
−
5
7
√
4
x=\frac{-3-\sqrt{57}}{4}
x=4−3−57
4
Solve
Rearrange and isolate the variable to find each solution
=
−
3
+
5
7
√
4
x=\frac{-3+\sqrt{57}}{4}
x=4−3+57
=
−
3
−
5
7
√
4
x=\frac{-3-\sqrt{57}}{4}
x=4−3−57
Solution
=
−
3
±
5
7
√
4