Answer:
The value of x is 6 or 4/5
Step-by-step explanation:
Consider the provided equation.
[tex]5x^2-34x=-24[/tex]
The above equation can be written as.
[tex]5x^2-34x+24=0[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a=5, b=-34 and c=24 in above formula.
[tex]x_{1,\:2}=\frac{-\left(-34\right)\pm \sqrt{\left(-34\right)^2-4\cdot \:5\cdot \:24}}{2\cdot \:5}[/tex]
[tex]x_{1,\:2}=\frac{34\pm \sqrt{1156-480}}{10}[/tex]
[tex]x_{1,\:2}=\frac{34\pm \sqrt{676}}{10}[/tex]
[tex]x_{1,\:2}=\frac{34\pm 26}{10}[/tex]
[tex]x_{1,\:2}=\frac{34\pm 26}{10}\\x_{1,\:2}=\frac{60}{10}\ or\ \frac{8}{10}\\x_{1,\:2}=6\ or\ \frac{4}{5}[/tex]
Hence, the value of x is 6 or 4/5
