10x(2x+9)=-3

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Solution for 10x(2x+9)=-3 equation:



10x(2x+9)=-3
We move all terms to the left:
10x(2x+9)-(-3)=0
We add all the numbers together, and all the variables
10x(2x+9)+3=0
We multiply parentheses
20x^2+90x+3=0
a = 20; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·20·3
Δ = 7860
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:
$\sqrt{\Delta}=\sqrt{7860}=\sqrt{4*1965}=\sqrt{4}*\sqrt{1965}=2\sqrt{1965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{1965}}{2*20}=\frac{-90-2\sqrt{1965}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{1965}}{2*20}=\frac{-90+2\sqrt{1965}}{40} $

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