4(0.5x+3)=5/2x+8

Solution for 4(0.5x+3)=5/2x+8 equation:

4(0.5x+3)=5/2x+8

We move all terms to the left:

4(0.5x+3)-(5/2x+8)=0


Domain of the equation: 2x+8)!=0

x∈R


We multiply parentheses

0x-(5/2x+8)+12=0

We get rid of parentheses

0x-5/2x-8+12=0

We multiply all the terms by the denominator


0x*2x-8*2x+12*2x-5=0

Wy multiply elements

0x^2-16x+24x-5=0

We add all the numbers together, and all the variables

x^2+8x-5=0

a = 1; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·1·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{21}}{2*1}=\frac{-8-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{21}}{2*1}=\frac{-8+2\sqrt{21}}{2}
$