Question

By using the formula, find the roots of the following quadratic equation, $(x+7)(x+3)=5(x+4)(x+2)+17x$

Answer 1

We have,

$(x+7)(x+3)=5(x+4)(x+2)+17x$

$x^2+10x+21=5x^2+47x+40$

$-4x^2-37x-19=0$

$4x^2+37x+19=0$

$a=4,b=37,c=19$

Since,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-\left(37\right)\pm \sqrt{{\left(37\right)}^2-4\left(4\right)\left(19\right)}}{2\left(4\right)}$

$=\frac{37\pm \sqrt{{\left(37\right)}^2-304}}{8}$

$\therefore x=\frac{37\pm \sqrt{1065}}{8}$

Hence, this is the answer.