10x+5+15x=5x(x+0.5)

Solution for 10x+5+15x=5x(x+0.5) equation:

10x+5+15x=5x(x+0.5)

We move all terms to the left:

10x+5+15x-(5x(x+0.5))=0

We add all the numbers together, and all the variables

25x-(5x(x+0.5))+5=0


We calculate terms in parentheses: -(5x(x+0.5)), so:

5x(x+0.5)

We multiply parentheses

5x^2+2.5x

Back to the equation:

-(5x^2+2.5x)


We get rid of parentheses

-5x^2+25x-2.5x+5=0

We add all the numbers together, and all the variables

-5x^2+22.5x+5=0

a = -5; b = 22.5; c = +5;
Δ = b2-4ac
Δ = 22.52-4·(-5)·5
Δ = 606.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22.5)-\sqrt{606.25}}{2*-5}=\frac{-22.5-\sqrt{606.25}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22.5)+\sqrt{606.25}}{2*-5}=\frac{-22.5+\sqrt{606.25}}{-10}
$