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(2x-1)(3x+2)=6x*6-x+2
We move all terms to the left:
(2x-1)(3x+2)-(6x*6-x+2)=0
We add all the numbers together, and all the variables
(2x-1)(3x+2)-(-1x+6x*6+2)=0
We get rid of parentheses
(2x-1)(3x+2)+1x-6x*6-2=0
We multiply parentheses ..
(+6x^2+4x-3x-2)+1x-6x*6-2=0
We add all the numbers together, and all the variables
(+6x^2+4x-3x-2)+x-6x*6-2=0
Wy multiply elements
(+6x^2+4x-3x-2)+x-36x-2=0
We get rid of parentheses
6x^2+4x-3x+x-36x-2-2=0
We add all the numbers together, and all the variables
6x^2-34x-4=0
a = 6; b = -34; c = -4;
Δ = b2-4ac
Δ = -342-4·6·(-4)
Δ = 1252
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{313}}{2*6}=\frac{34-2\sqrt{313}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{313}}{2*6}=\frac{34+2\sqrt{313}}{12} $
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