7x(x-2)+3=2x+5(-2+x)

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Solution for 7x(x-2)+3=2x+5(-2+x) equation: 



7x(x-2)+3=2x+5(-2+x)

We move all terms to the left:

7x(x-2)+3-(2x+5(-2+x))=0

We add all the numbers together, and all the variables

7x(x-2)-(2x+5(x-2))+3=0

We multiply parentheses

7x^2-14x-(2x+5(x-2))+3=0



We calculate terms in parentheses: -(2x+5(x-2)), so:

2x+5(x-2)

We multiply parentheses

2x+5x-10

We add all the numbers together, and all the variables

7x-10

Back to the equation:

-(7x-10)



We get rid of parentheses

7x^2-14x-7x+10+3=0

We add all the numbers together, and all the variables

7x^2-21x+13=0

a = 7; b = -21; c = +13;
Δ = b2-4ac
Δ = -212-4·7·13
Δ = 77
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{-(-21)-\sqrt{77}}{2*7}=\frac{21-\sqrt{77}}{14}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{77}}{2*7}=\frac{21+\sqrt{77}}{14}
$

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