2.1x(x+5)=3.4(5x+10)

Solution for 2.1x(x+5)=3.4(5x+10) equation:

2.1x(x+5)=3.4(5x+10)

We move all terms to the left:

2.1x(x+5)-(3.4(5x+10))=0

We multiply parentheses

2x^2+10x-(3.4(5x+10))=0


We calculate terms in parentheses: -(3.4(5x+10)), so:

3.4(5x+10)

We multiply parentheses

17x+34

Back to the equation:

-(17x+34)


We get rid of parentheses

2x^2+10x-17x-34=0

We add all the numbers together, and all the variables

2x^2-7x-34=0

a = 2; b = -7; c = -34;
Δ = b2-4ac
Δ = -72-4·2·(-34)
Δ = 321
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{-(-7)-\sqrt{321}}{2*2}=\frac{7-\sqrt{321}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{321}}{2*2}=\frac{7+\sqrt{321}}{4}
$