Answer
$x=-\displaystyle \frac{3}{2}+\frac{\sqrt{37}}{2}$ or $x=-\displaystyle \frac{3}{2}-\frac{\sqrt{37}}{2}$
Work Step by Step
$ 5x(x-1)-7=4x(x-2)\qquad$... use the distributive property: $a(b+c)=ab+ac$.
$ 5x^{2}-5x-7=4x^{2}-8x\qquad$...add $(-4x^{2}+8x)$ to both sides.
$ 5x^{2}-5x-7-4x^{2}+8x=4x^{2}-8x-4x^{2}+8x\qquad$...add like terms.
$ x^{2}+3x-7=0\qquad$... solve with the Quadractic formula. $a=1,\ b=3,\ c=-7$
$ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $3,\ a$ for $1$ and $c$ for $-7$.
$ x=\displaystyle \frac{-3\pm\sqrt{(3)^{2}-4\cdot(-7)\cdot 1}}{2\cdot 1}\qquad$... simplify.
$x=\displaystyle \frac{-3\pm\sqrt{9+28}}{2}$
$ x=\displaystyle \frac{-3\pm\sqrt{37}}{2}\qquad$... the symbol $\pm$ indicates two solutions.
$x=-\displaystyle \frac{3}{2}+\frac{\sqrt{37}}{2}$ or $x=-\displaystyle \frac{3}{2}-\frac{\sqrt{37}}{2}$
