5x+10=3x(x+10)

Solution for 5x+10=3x(x+10) equation:

5x+10=3x(x+10)

We move all terms to the left:

5x+10-(3x(x+10))=0


We calculate terms in parentheses: -(3x(x+10)), so:

3x(x+10)

We multiply parentheses

3x^2+30x

Back to the equation:

-(3x^2+30x)


We get rid of parentheses

-3x^2+5x-30x+10=0

We add all the numbers together, and all the variables

-3x^2-25x+10=0

a = -3; b = -25; c = +10;
Δ = b2-4ac
Δ = -252-4·(-3)·10
Δ = 745
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{-(-25)-\sqrt{745}}{2*-3}=\frac{25-\sqrt{745}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{745}}{2*-3}=\frac{25+\sqrt{745}}{-6}
$