(5x-12)(2x+1)=-18

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Solution for (5x-12)(2x+1)=-18 equation:



(5x-12)(2x+1)=-18
We move all terms to the left:
(5x-12)(2x+1)-(-18)=0
We add all the numbers together, and all the variables
(5x-12)(2x+1)+18=0
We multiply parentheses ..
(+10x^2+5x-24x-12)+18=0
We get rid of parentheses
10x^2+5x-24x-12+18=0
We add all the numbers together, and all the variables
10x^2-19x+6=0
a = 10; b = -19; c = +6;
Δ = b2-4ac
Δ = -192-4·10·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-11}{2*10}=\frac{8}{20} =2/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+11}{2*10}=\frac{30}{20} =1+1/2 $

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