2x(5x+9)=4(6x+10)

Solution for 2x(5x+9)=4(6x+10) equation:

2x(5x+9)=4(6x+10)

We move all terms to the left:

2x(5x+9)-(4(6x+10))=0

We multiply parentheses

10x^2+18x-(4(6x+10))=0


We calculate terms in parentheses: -(4(6x+10)), so:

4(6x+10)

We multiply parentheses

24x+40

Back to the equation:

-(24x+40)


We get rid of parentheses

10x^2+18x-24x-40=0

We add all the numbers together, and all the variables

10x^2-6x-40=0

a = 10; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·10·(-40)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{409}}{2*10}=\frac{6-2\sqrt{409}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{409}}{2*10}=\frac{6+2\sqrt{409}}{20}
$