1/2*4x+10=5-3x

Solution for 1/2*4x+10=5-3x equation:

1/2*4x+10=5-3x

We move all terms to the left:

1/2*4x+10-(5-3x)=0


Domain of the equation: 2*4x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2*4x-(-3x+5)+10=0

We get rid of parentheses

1/2*4x+3x-5+10=0

We multiply all the terms by the denominator


3x*2*4x-5*2*4x+10*2*4x+1=0

Wy multiply elements

24x^2*4-40x*4+80x*4+1=0

Wy multiply elements

96x^2-160x+320x+1=0

We add all the numbers together, and all the variables

96x^2+160x+1=0

a = 96; b = 160; c = +1;
Δ = b2-4ac
Δ = 1602-4·96·1
Δ = 25216
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:

$\sqrt{\Delta}=\sqrt{25216}=\sqrt{64*394}=\sqrt{64}*\sqrt{394}=8\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-8\sqrt{394}}{2*96}=\frac{-160-8\sqrt{394}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+8\sqrt{394}}{2*96}=\frac{-160+8\sqrt{394}}{192}
$