3(0.4x-2)+4(x+3)=4/5x-5

Solution for 3(0.4x-2)+4(x+3)=4/5x-5 equation:

3(0.4x-2)+4(x+3)=4/5x-5

We move all terms to the left:

3(0.4x-2)+4(x+3)-(4/5x-5)=0


Domain of the equation: 5x-5)!=0

x∈R


We multiply parentheses

0x+4x-(4/5x-5)-6+12=0

We get rid of parentheses

0x+4x-4/5x+5-6+12=0

We multiply all the terms by the denominator


0x*5x+4x*5x+5*5x-6*5x+12*5x-4=0

Wy multiply elements

0x^2+20x^2+25x-30x+60x-4=0

We add all the numbers together, and all the variables

21x^2+55x-4=0

a = 21; b = 55; c = -4;
Δ = b2-4ac
Δ = 552-4·21·(-4)
Δ = 3361
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{-(55)-\sqrt{3361}}{2*21}=\frac{-55-\sqrt{3361}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3361}}{2*21}=\frac{-55+\sqrt{3361}}{42}
$