1/2*6x-10+x=15

Solution for 1/2*6x-10+x=15 equation:

1/2*6x-10+x=15

We move all terms to the left:

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


Domain of the equation: 2*6x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2*6x-25=0

We multiply all the terms by the denominator


x*2*6x-25*2*6x+1=0

Wy multiply elements

12x^2*6-300x*6+1=0

Wy multiply elements

72x^2-1800x+1=0

a = 72; b = -1800; c = +1;
Δ = b2-4ac
Δ = -18002-4·72·1
Δ = 3239712
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:

$\sqrt{\Delta}=\sqrt{3239712}=\sqrt{144*22498}=\sqrt{144}*\sqrt{22498}=12\sqrt{22498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1800)-12\sqrt{22498}}{2*72}=\frac{1800-12\sqrt{22498}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1800)+12\sqrt{22498}}{2*72}=\frac{1800+12\sqrt{22498}}{144}
$