x(4x-15)=407.43

Solution for x(4x-15)=407.43 equation:

x(4x-15)=407.43

We move all terms to the left:

x(4x-15)-(407.43)=0

We add all the numbers together, and all the variables

x(4x-15)-407.43=0

We multiply parentheses

4x^2-15x-407.43=0

a = 4; b = -15; c = -407.43;
Δ = b2-4ac
Δ = -152-4·4·(-407.43)
Δ = 6743.88
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{-(-15)-\sqrt{6743.88}}{2*4}=\frac{15-\sqrt{6743.88}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{6743.88}}{2*4}=\frac{15+\sqrt{6743.88}}{8}
$