2x-5=3x(0.5x+4)

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

2x-5=3x(0.5x+4)

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(0.5x+4)), so:

3x(0.5x+4)

We multiply parentheses

0x^2+12x

We add all the numbers together, and all the variables

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2+2x-12x-5=0

We add all the numbers together, and all the variables

-1x^2-10x-5=0

a = -1; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·(-1)·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*-1}=\frac{10-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*-1}=\frac{10+4\sqrt{5}}{-2}
$