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(11x-15)(5x-13)=180
We move all terms to the left:
(11x-15)(5x-13)-(180)=0
We multiply parentheses ..
(+55x^2-143x-75x+195)-180=0
We get rid of parentheses
55x^2-143x-75x+195-180=0
We add all the numbers together, and all the variables
55x^2-218x+15=0
a = 55; b = -218; c = +15;
Δ = b2-4ac
Δ = -2182-4·55·15
Δ = 44224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44224}=\sqrt{64*691}=\sqrt{64}*\sqrt{691}=8\sqrt{691}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-8\sqrt{691}}{2*55}=\frac{218-8\sqrt{691}}{110} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+8\sqrt{691}}{2*55}=\frac{218+8\sqrt{691}}{110} $
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