1/2x+34-2(x+5)=3x-11

Solution for 1/2x+34-2(x+5)=3x-11 equation:

1/2x+34-2(x+5)=3x-11

We move all terms to the left:

1/2x+34-2(x+5)-(3x-11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x-2x-(3x-11)-10+34=0

We get rid of parentheses

1/2x-2x-3x+11-10+34=0

We multiply all the terms by the denominator


-2x*2x-3x*2x+11*2x-10*2x+34*2x+1=0

Wy multiply elements

-4x^2-6x^2+22x-20x+68x+1=0

We add all the numbers together, and all the variables

-10x^2+70x+1=0

a = -10; b = 70; c = +1;
Δ = b2-4ac
Δ = 702-4·(-10)·1
Δ = 4940
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:

$\sqrt{\Delta}=\sqrt{4940}=\sqrt{4*1235}=\sqrt{4}*\sqrt{1235}=2\sqrt{1235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1235}}{2*-10}=\frac{-70-2\sqrt{1235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1235}}{2*-10}=\frac{-70+2\sqrt{1235}}{-20}
$