10x(x+2)=3(3x+7)

Solution for 10x(x+2)=3(3x+7) equation:

10x(x+2)=3(3x+7)

We move all terms to the left:

10x(x+2)-(3(3x+7))=0

We multiply parentheses

10x^2+20x-(3(3x+7))=0


We calculate terms in parentheses: -(3(3x+7)), so:

3(3x+7)

We multiply parentheses

9x+21

Back to the equation:

-(9x+21)


We get rid of parentheses

10x^2+20x-9x-21=0

We add all the numbers together, and all the variables

10x^2+11x-21=0

a = 10; b = 11; c = -21;
Δ = b2-4ac
Δ = 112-4·10·(-21)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-31}{2*10}=\frac{-42}{20}
=-2+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*10}=\frac{20}{20}
=1
$