-0.75+0.4x=7/20x-0.5

Solution for -0.75+0.4x=7/20x-0.5 equation:

-0.75+0.4x=7/20x-0.5

We move all terms to the left:

-0.75+0.4x-(7/20x-0.5)=0


Domain of the equation: 20x-0.5)!=0

x∈R


We get rid of parentheses

0.4x-7/20x+0.5-0.75=0

We multiply all the terms by the denominator


(0.4x)*20x+(0.5)*20x-(0.75)*20x-7=0

We add all the numbers together, and all the variables

(+0.4x)*20x+(0.5)*20x-(0.75)*20x-7=0

We multiply parentheses

0x^2+10x-15x-7=0

We add all the numbers together, and all the variables

x^2-5x-7=0

a = 1; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·1·(-7)
Δ = 53
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{53}}{2*1}=\frac{5-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*1}=\frac{5+\sqrt{53}}{2}
$