Answer
$x\approx1.19$ and
$x\approx-4.19$
Work Step by Step
$4x^{2}+12x-15=5$
Adding $15$ to both sides, we get
$4x^{2}+12x=20$
Divide both sides of the equation by $4$ to obtain
$x^{2}+3x=5$
Add $(\frac{b}{2})^{2}=(\frac{3}{2})^{2}$ to both sides to complete the square.
$x^{2}+3x+(\frac{3}{2})^{2}=5+(\frac{3}{2})^{2}$
$\implies (x+\frac{3}{2})^{2}=5+\frac{9}{4}$
$\implies (x+\frac{3}{2})^{2}=\frac{29}{4}$
Taking square root on both sides, we have
$x+\frac{3}{2}=\pm\frac{\sqrt {29}}{2}$
$\implies x=-\frac{3}{2}\pm \frac{\sqrt {29}}{2}$
The solutions of the given equation are $x=-\frac{3}{2}+\frac{\sqrt {29}}{2}\approx1.19$ and
$x=-\frac{3}{2}-\frac{\sqrt {29}}{2}\approx-4.19$
