For a quadratic equation of the form:
[tex]av^2+bv+c=0[/tex]
The quadratic formula is:
[tex]v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]
In this case, we have the eqaution:
[tex]11v^2+8v=4[/tex]
First, let's rest 4 on both sides to get 0 in the right hand side:
[tex]11v^2+8v-4=0[/tex]
Then we can use the quadratic formula:
[tex]v_{1,2}=\frac{-8\pm\sqrt[]{8^2-4\cdot11\cdot(-4)}}{2\cdot11}[/tex]
And solve:
[tex]\begin{gathered} v_{1,2}=\frac{-8\pm\sqrt[]{64^{}+176}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{240}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{16}\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-8\pm4\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-4\pm2\sqrt[]{15}}{11} \end{gathered}[/tex]
Then the two solutions are:
[tex]\begin{gathered} v_1=\frac{-4-2\sqrt[]{15}}{11} \\ v_2=\frac{-4+2\sqrt[]{15}}{11} \end{gathered}[/tex]
