$x-3{x}^{2}+4x+3=0$
Collect like terms$5x-3{x}^{2}+3=0$
Use the commutative property to reorder the terms$-3{x}^{2}+5x+3=0$
Change the signs on both sides of the equation$3{x}^{2}-5x-3=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=3,& b=-5,& c=-3\end{array}$
Substitute $a=3$, $b=-5$ and $c=-3$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 3 \times \left( -3 \right) } }{ 2 \times 3 }$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$x=\frac{ 5\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 3 \times \left( -3 \right) } }{ 2 \times 3 }$
Evaluate the power$x=\frac{ 5\pm\sqrt{ 25-4 \times 3 \times \left( -3 \right) } }{ 2 \times 3 }$
Calculate the product$x=\frac{ 5\pm\sqrt{ 25+36 } }{ 2 \times 3 }$
Multiply the numbers$x=\frac{ 5\pm\sqrt{ 25+36 } }{ 6 }$
Add the numbers$x=\frac{ 5\pm\sqrt{ 61 } }{ 6 }$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }x=\frac{ 5+\sqrt{ 61 } }{ 6 },\\x=\frac{ 5-\sqrt{ 61 } }{ 6 }\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }x_1=\frac{ 5-\sqrt{ 61 } }{ 6 },& x_2=\frac{ 5+\sqrt{ 61 } }{ 6 }\end{array} \\&\begin{array} { l }x_1\approx-0.468375,& x_2\approx2.13504\end{array}\end{align*}$