1.54=9.8x^2+11.6x

Solution for 1.54=9.8x^2+11.6x equation:

1.54=9.8x^2+11.6x

We move all terms to the left:

1.54-(9.8x^2+11.6x)=0

We get rid of parentheses

-9.8x^2-11.6x+1.54=0

a = -9.8; b = -11.6; c = +1.54;
Δ = b2-4ac
Δ = -11.62-4·(-9.8)·1.54
Δ = 194.928
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11.6)-\sqrt{194.928}}{2*-9.8}=\frac{11.6-\sqrt{194.928}}{-19.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.6)+\sqrt{194.928}}{2*-9.8}=\frac{11.6+\sqrt{194.928}}{-19.6}
$