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(2x-11)(5x-39)=90
We move all terms to the left:
(2x-11)(5x-39)-(90)=0
We multiply parentheses ..
(+10x^2-78x-55x+429)-90=0
We get rid of parentheses
10x^2-78x-55x+429-90=0
We add all the numbers together, and all the variables
10x^2-133x+339=0
a = 10; b = -133; c = +339;
Δ = b2-4ac
Δ = -1332-4·10·339
Δ = 4129
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{-(-133)-\sqrt{4129}}{2*10}=\frac{133-\sqrt{4129}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+\sqrt{4129}}{2*10}=\frac{133+\sqrt{4129}}{20} $
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