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2(12+2x)-(3x-2)(3x-2)/5=20
We move all terms to the left:
2(12+2x)-(3x-2)(3x-2)/5-(20)=0
We add all the numbers together, and all the variables
2(2x+12)-(3x-2)(3x-2)/5-20=0
We multiply parentheses
4x-(3x-2)(3x-2)/5+24-20=0
We multiply parentheses ..
-(+9x^2-6x-6x+4)/5+4x+24-20=0
We multiply all the terms by the denominator
-(+9x^2-6x-6x+4)+4x*5+24*5-20*5=0
We add all the numbers together, and all the variables
-(+9x^2-6x-6x+4)+4x*5+20=0
Wy multiply elements
-(+9x^2-6x-6x+4)+20x+20=0
We get rid of parentheses
-9x^2+6x+6x+20x-4+20=0
We add all the numbers together, and all the variables
-9x^2+32x+16=0
a = -9; b = 32; c = +16;
Δ = b2-4ac
Δ = 322-4·(-9)·16
Δ = 1600
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{1600}=40$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-40}{2*-9}=\frac{-72}{-18} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+40}{2*-9}=\frac{8}{-18} =-4/9 $
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