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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-(2(4-x)+10)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -(2(-1x+4)+10), so:

2(-1x+4)+10

We multiply parentheses

-2x+8+10

We add all the numbers together, and all the variables

-2x+18

Back to the equation:

-(-2x+18)


We add all the numbers together, and all the variables

x*2x-(-2x+18)=0

Wy multiply elements

2x^2-(-2x+18)=0

We get rid of parentheses

2x^2+2x-18=0

a = 2; b = 2; c = -18;
Δ = b2-4ac
Δ = 22-4·2·(-18)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*2}=\frac{-2-2\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*2}=\frac{-2+2\sqrt{37}}{4}
$