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(4x-5)(x-3)-(3x+1)(4x-5)=0
We multiply parentheses ..
(+4x^2-12x-5x+15)-(3x+1)(4x-5)=0
We get rid of parentheses
4x^2-12x-5x-(3x+1)(4x-5)+15=0
We multiply parentheses ..
4x^2-(+12x^2-15x+4x-5)-12x-5x+15=0
We add all the numbers together, and all the variables
4x^2-(+12x^2-15x+4x-5)-17x+15=0
We get rid of parentheses
4x^2-12x^2+15x-4x-17x+5+15=0
We add all the numbers together, and all the variables
-8x^2-6x+20=0
a = -8; b = -6; c = +20;
Δ = b2-4ac
Δ = -62-4·(-8)·20
Δ = 676
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{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-26}{2*-8}=\frac{-20}{-16} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+26}{2*-8}=\frac{32}{-16} =-2 $
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