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(15x-19)(11x-3)=41
We move all terms to the left:
(15x-19)(11x-3)-(41)=0
We multiply parentheses ..
(+165x^2-45x-209x+57)-41=0
We get rid of parentheses
165x^2-45x-209x+57-41=0
We add all the numbers together, and all the variables
165x^2-254x+16=0
a = 165; b = -254; c = +16;
Δ = b2-4ac
Δ = -2542-4·165·16
Δ = 53956
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{53956}=\sqrt{4*13489}=\sqrt{4}*\sqrt{13489}=2\sqrt{13489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-254)-2\sqrt{13489}}{2*165}=\frac{254-2\sqrt{13489}}{330} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-254)+2\sqrt{13489}}{2*165}=\frac{254+2\sqrt{13489}}{330} $
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