-3(x-5)=4(-x+1/2)

Solution for -3(x-5)=4(-x+1/2) equation:

-3(x-5)=4(-x+1/2)

We move all terms to the left:

-3(x-5)-(4(-x+1/2))=0

We add all the numbers together, and all the variables

-3(x-5)-(4(-1x+1/2))=0

We multiply parentheses

-3x-(4(-1x+1/2))+15=0

We multiply all the terms by the denominator


-3x*2))-(4(-1x+1+15*2))=0

We add all the numbers together, and all the variables

-3x*2))-(4(-1x+31))=0

We add all the numbers together, and all the variables

-1x-3x*2))-(4(=0

Wy multiply elements

-6x^2-1x=0

a = -6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-6}=\frac{2}{-12}
=-1/6
$