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3(x+4)(x-2)-2(x-5)(x-3)=5
We move all terms to the left:
3(x+4)(x-2)-2(x-5)(x-3)-(5)=0
We multiply parentheses ..
3(+x^2-2x+4x-8)-2(x-5)(x-3)-5=0
We multiply parentheses
3x^2-6x+12x-2(x-5)(x-3)-24-5=0
We multiply parentheses ..
3x^2-2(+x^2-3x-5x+15)-6x+12x-24-5=0
We add all the numbers together, and all the variables
3x^2-2(+x^2-3x-5x+15)+6x-29=0
We multiply parentheses
3x^2-2x^2+6x+10x+6x-30-29=0
We add all the numbers together, and all the variables
x^2+22x-59=0
a = 1; b = 22; c = -59;
Δ = b2-4ac
Δ = 222-4·1·(-59)
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12\sqrt{5}}{2*1}=\frac{-22-12\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12\sqrt{5}}{2*1}=\frac{-22+12\sqrt{5}}{2} $
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