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(2x-1)(x+3)+(1-2x)(4x-3)=0
We add all the numbers together, and all the variables
(2x-1)(x+3)+(-2x+1)(4x-3)=0
We multiply parentheses ..
(+2x^2+6x-1x-3)+(-2x+1)(4x-3)=0
We get rid of parentheses
2x^2+6x-1x+(-2x+1)(4x-3)-3=0
We multiply parentheses ..
2x^2+(-8x^2+6x+4x-3)+6x-1x-3=0
We add all the numbers together, and all the variables
2x^2+(-8x^2+6x+4x-3)+5x-3=0
We get rid of parentheses
2x^2-8x^2+6x+4x+5x-3-3=0
We add all the numbers together, and all the variables
-6x^2+15x-6=0
a = -6; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-6)·(-6)
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*-6}=\frac{-24}{-12} =+2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-6}=\frac{-6}{-12} =1/2 $
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