2(0.8x-3)=8/5x-7

Solution for 2(0.8x-3)=8/5x-7 equation:

2(0.8x-3)=8/5x-7

We move all terms to the left:

2(0.8x-3)-(8/5x-7)=0


Domain of the equation: 5x-7)!=0

x∈R


We multiply parentheses

0x-(8/5x-7)-6=0

We get rid of parentheses

0x-8/5x+7-6=0

We multiply all the terms by the denominator


0x*5x+7*5x-6*5x-8=0

Wy multiply elements

0x^2+35x-30x-8=0

We add all the numbers together, and all the variables

x^2+5x-8=0

a = 1; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·1·(-8)
Δ = 57
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{-(5)-\sqrt{57}}{2*1}=\frac{-5-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*1}=\frac{-5+\sqrt{57}}{2}
$