3x-(1/2)(10x+6)=15

Solution for 3x-(1/2)(10x+6)=15 equation:

3x-(1/2)(10x+6)=15

We move all terms to the left:

3x-(1/2)(10x+6)-(15)=0


Domain of the equation: 2)(10x+6)!=0

x∈R


We add all the numbers together, and all the variables

3x-(+1/2)(10x+6)-15=0

We multiply parentheses ..

-(+10x^2+1/2*6)+3x-15=0

We multiply all the terms by the denominator


-(+10x^2+1+3x*2*6)-15*2*6)=0

We add all the numbers together, and all the variables

-(+10x^2+1+3x*2*6)=0

We get rid of parentheses

-10x^2-3x*2*6-1=0

Wy multiply elements

-10x^2-36x*6-1=0

Wy multiply elements

-10x^2-216x-1=0

a = -10; b = -216; c = -1;
Δ = b2-4ac
Δ = -2162-4·(-10)·(-1)
Δ = 46616
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:

$\sqrt{\Delta}=\sqrt{46616}=\sqrt{4*11654}=\sqrt{4}*\sqrt{11654}=2\sqrt{11654}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-2\sqrt{11654}}{2*-10}=\frac{216-2\sqrt{11654}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+2\sqrt{11654}}{2*-10}=\frac{216+2\sqrt{11654}}{-20}
$