30x-0.1x^2-7x-400=0

Solution for 30x-0.1x^2-7x-400=0 equation:

30x-0.1x^2-7x-400=0

We add all the numbers together, and all the variables

-0.1x^2+23x-400=0

a = -0.1; b = 23; c = -400;
Δ = b2-4ac
Δ = 232-4·(-0.1)·(-400)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-3\sqrt{41}}{2*-0.1}=\frac{-23-3\sqrt{41}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+3\sqrt{41}}{2*-0.1}=\frac{-23+3\sqrt{41}}{-0.2}
$