(3/4)x-1/2=10-x

Solution for (3/4)x-1/2=10-x equation:

(3/4)x-1/2=10-x

We move all terms to the left:

(3/4)x-1/2-(10-x)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x-(-1x+10)-1/2=0

We multiply parentheses

3x^2-(-1x+10)-1/2=0

We get rid of parentheses

3x^2+1x-10-1/2=0

We multiply all the terms by the denominator


3x^2*2+1x*2-1-10*2=0

We add all the numbers together, and all the variables

3x^2*2+1x*2-21=0

Wy multiply elements

6x^2+2x-21=0

a = 6; b = 2; c = -21;
Δ = b2-4ac
Δ = 22-4·6·(-21)
Δ = 508
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{127}}{2*6}=\frac{-2-2\sqrt{127}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{127}}{2*6}=\frac{-2+2\sqrt{127}}{12}
$