Answer
The solutions are $\frac{6}{5}$ and $\frac{-5}{6}$.
Work Step by Step
30$x^{2}$-11x=30
30$x^{2}$-11x-30=30-30
30$x^{2}$-11x-30=0
30$x^{2}$+25x-36x-30=0
5x(6x+5)-6(6x+5)=0
(5x-6)(6x+5)=0
(5x-6) =0 or (6x+5)=0
5x-6+6=0+6 or 6x+5-5=0-5
5x=6 or 6x=-5
x=$\frac{6}{5}$ or x=$\frac{-5}{6}$
The solutions are $\frac{6}{5}$ and $\frac{-5}{6}$.
Check
Let x= $\frac{6}{5}$
30$x^{2}$-11x=30
30$(6/5)^{2}$-11$\frac{6}{5}$=30
30*36/25-$\frac{66}{5}$=30
6*36/5-$\frac{66}{5}$=30
216/5-$\frac{66}{5}$=30
150/5=30
30=30
Let x= $\frac{-5}{6}$
30$x^{2}$-11x=30
30$(-5/6)^{2}$-11$\frac{-5}{6}$=30
30*25/36+$\frac{55}{6}$=30
5*25/6+$\frac{55}{6}$=30
125/6+$\frac{55}{6}$=30
180/6=30
30=30
