5x(2x+1)+7(4x+2)=0

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Solution for 5x(2x+1)+7(4x+2)=0 equation:



5x(2x+1)+7(4x+2)=0
We multiply parentheses
10x^2+5x+28x+14=0
We add all the numbers together, and all the variables
10x^2+33x+14=0
a = 10; b = 33; c = +14;
Δ = b2-4ac
Δ = 332-4·10·14
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-23}{2*10}=\frac{-56}{20} =-2+4/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+23}{2*10}=\frac{-10}{20} =-1/2 $

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