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(11x-15)(5x-13)=x
We move all terms to the left:
(11x-15)(5x-13)-(x)=0
We add all the numbers together, and all the variables
-1x+(11x-15)(5x-13)=0
We multiply parentheses ..
(+55x^2-143x-75x+195)-1x=0
We get rid of parentheses
55x^2-143x-75x-1x+195=0
We add all the numbers together, and all the variables
55x^2-219x+195=0
a = 55; b = -219; c = +195;
Δ = b2-4ac
Δ = -2192-4·55·195
Δ = 5061
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-219)-\sqrt{5061}}{2*55}=\frac{219-\sqrt{5061}}{110} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-219)+\sqrt{5061}}{2*55}=\frac{219+\sqrt{5061}}{110} $
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