0.4x-3/1.5x+9=-75

Solution for 0.4x-3/1.5x+9=-75 equation:

0.4x-3/1.5x+9=-75

We move all terms to the left:

0.4x-3/1.5x+9-(-75)=0


Domain of the equation: 1.5x!=0

x!=0/1.5

x!=0

x∈R


We add all the numbers together, and all the variables

0.4x-3/1.5x+84=0

We multiply all the terms by the denominator


(0.4x)*1.5x+84*1.5x-3=0

We add all the numbers together, and all the variables

(+0.4x)*1.5x+84*1.5x-3=0

We multiply parentheses

0x^2+84*1.5x-3=0

Wy multiply elements

0x^2+84x-3=0

We add all the numbers together, and all the variables

x^2+84x-3=0

a = 1; b = 84; c = -3;
Δ = b2-4ac
Δ = 842-4·1·(-3)
Δ = 7068
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:

$\sqrt{\Delta}=\sqrt{7068}=\sqrt{4*1767}=\sqrt{4}*\sqrt{1767}=2\sqrt{1767}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1767}}{2*1}=\frac{-84-2\sqrt{1767}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1767}}{2*1}=\frac{-84+2\sqrt{1767}}{2}
$