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(x-5)(3x-5)=x-11
We move all terms to the left:
(x-5)(3x-5)-(x-11)=0
We get rid of parentheses
(x-5)(3x-5)-x+11=0
We multiply parentheses ..
(+3x^2-5x-15x+25)-x+11=0
We add all the numbers together, and all the variables
(+3x^2-5x-15x+25)-1x+11=0
We get rid of parentheses
3x^2-5x-15x-1x+25+11=0
We add all the numbers together, and all the variables
3x^2-21x+36=0
a = 3; b = -21; c = +36;
Δ = b2-4ac
Δ = -212-4·3·36
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*3}=\frac{18}{6} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*3}=\frac{24}{6} =4 $
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