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(4x-3)(5x-3)+(8x-7)(3x-1)=0
We multiply parentheses ..
(+20x^2-12x-15x+9)+(8x-7)(3x-1)=0
We get rid of parentheses
20x^2-12x-15x+(8x-7)(3x-1)+9=0
We multiply parentheses ..
20x^2+(+24x^2-8x-21x+7)-12x-15x+9=0
We add all the numbers together, and all the variables
20x^2+(+24x^2-8x-21x+7)-27x+9=0
We get rid of parentheses
20x^2+24x^2-8x-21x-27x+7+9=0
We add all the numbers together, and all the variables
44x^2-56x+16=0
a = 44; b = -56; c = +16;
Δ = b2-4ac
Δ = -562-4·44·16
Δ = 320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{5}}{2*44}=\frac{56-8\sqrt{5}}{88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{5}}{2*44}=\frac{56+8\sqrt{5}}{88} $
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