2x(x-15)=-3

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Solution for 2x(x-15)=-3 equation:



2x(x-15)=-3
We move all terms to the left:
2x(x-15)-(-3)=0
We add all the numbers together, and all the variables
2x(x-15)+3=0
We multiply parentheses
2x^2-30x+3=0
a = 2; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·2·3
Δ = 876
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:
$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*2}=\frac{30-2\sqrt{219}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*2}=\frac{30+2\sqrt{219}}{4} $

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