2x+5=3x(x+10)

Solution for 2x+5=3x(x+10) equation:

2x+5=3x(x+10)

We move all terms to the left:

2x+5-(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+2x-30x+5=0

We add all the numbers together, and all the variables

-3x^2-28x+5=0

a = -3; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·(-3)·5
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{211}}{2*-3}=\frac{28-2\sqrt{211}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{211}}{2*-3}=\frac{28+2\sqrt{211}}{-6}
$