(5x+2)*(x+2)=7

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



(5x+2)(x+2)=7
We move all terms to the left:
(5x+2)(x+2)-(7)=0
We multiply parentheses ..
(+5x^2+10x+2x+4)-7=0
We get rid of parentheses
5x^2+10x+2x+4-7=0
We add all the numbers together, and all the variables
5x^2+12x-3=0
a = 5; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·5·(-3)
Δ = 204
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:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*5}=\frac{-12-2\sqrt{51}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*5}=\frac{-12+2\sqrt{51}}{10} $

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