3/4x=x-0.3

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Solution for 3/4x=x-0.3 equation: 



3/4x=x-0.3

We move all terms to the left:

3/4x-(x-0.3)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We get rid of parentheses

3/4x-x+0.3=0

We multiply all the terms by the denominator


-x*4x+(0.3)*4x+3=0

We multiply parentheses

-x*4x+1.2x+3=0

Wy multiply elements

-4x^2+1.2x+3=0

a = -4; b = 1.2; c = +3;
Δ = b2-4ac
Δ = 1.22-4·(-4)·3
Δ = 49.44
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{-(1.2)-\sqrt{49.44}}{2*-4}=\frac{-1.2-\sqrt{49.44}}{-8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.2)+\sqrt{49.44}}{2*-4}=\frac{-1.2+\sqrt{49.44}}{-8}
$

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