Answer
$x = 1, -2.500$
Work Step by Step
$4x^{2} + 6x - 10 = 0$
$2(2x^{2} + 3x - 5) = 0$
$2(2x^{2} + 5x - 2x - 5) = 0$
$2(x(2x+5) - 1(2x + 5)) = 0$
$2(x-1)(2x+5) = 0$
$x = 1, -\frac{5}{2}$
$x = 1, -2.500$
$2x + 5 = 0$
$2x = -5$
$x = -\frac{5}{2}$
Check:
When $x = 1$
$4x^{2} + 6x - 10 \overset{?}{=} 0$
$4(1)^{2} + 6(1) - 10 \overset{?}{=} 0$
$4 + 6 - 10 \overset{?}{=} 0$
$10 - 10 \overset{?}{=} 0$
$0 = 0$
When $x = -\frac{5}{2}$
$4x^{2} + 6x - 10 \overset{?}{=} 0$
$4(-\frac{5}{2})^{2} + 6(-\frac{5}{2}) - 10 \overset{?}{=} 0$
$4(6.25) - 15 - 10 \overset{?}{=} 0$
$25 - 15 - 10 \overset{?}{=} 0$
$25 - 25 \overset{?}{=} 0$
$0 = 0$
