X(150+4.9x)=8

Solution for X(150+4.9x)=8 equation:

X(150+4.9X)=8

We move all terms to the left:

X(150+4.9X)-(8)=0

We add all the numbers together, and all the variables

X(4.9X+150)-8=0

We multiply parentheses

4X^2+150X-8=0

a = 4; b = 150; c = -8;
Δ = b2-4ac
Δ = 1502-4·4·(-8)
Δ = 22628
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{22628}=\sqrt{4*5657}=\sqrt{4}*\sqrt{5657}=2\sqrt{5657}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5657}}{2*4}=\frac{-150-2\sqrt{5657}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5657}}{2*4}=\frac{-150+2\sqrt{5657}}{8}
$