-3x+(1/2)(-6x+11)=-3.5

Solution for -3x+(1/2)(-6x+11)=-3.5 equation:

-3x+(1/2)(-6x+11)=-3.5

We move all terms to the left:

-3x+(1/2)(-6x+11)-(-3.5)=0


Domain of the equation: 2)(-6x+11)!=0

x∈R


We add all the numbers together, and all the variables

-3x+(+1/2)(-6x+11)-(-3.5)=0

We add all the numbers together, and all the variables

-3x+(+1/2)(-6x+11)+3.5=0

We multiply parentheses ..

(-6x^2+1/2*11)-3x+3.5=0

We multiply all the terms by the denominator


(-6x^2+1-3x*2*11)+(3.5)*2*11)=0

We add all the numbers together, and all the variables

(-6x^2+1-3x*2*11)=0

We get rid of parentheses

-6x^2-3x*2*11+1=0

Wy multiply elements

-6x^2-66x*1+1=0

Wy multiply elements

-6x^2-66x+1=0

a = -6; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·(-6)·1
Δ = 4380
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:

$\sqrt{\Delta}=\sqrt{4380}=\sqrt{4*1095}=\sqrt{4}*\sqrt{1095}=2\sqrt{1095}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1095}}{2*-6}=\frac{66-2\sqrt{1095}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1095}}{2*-6}=\frac{66+2\sqrt{1095}}{-12}
$