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(11x-3)(4x+39)=90
We move all terms to the left:
(11x-3)(4x+39)-(90)=0
We multiply parentheses ..
(+44x^2+429x-12x-117)-90=0
We get rid of parentheses
44x^2+429x-12x-117-90=0
We add all the numbers together, and all the variables
44x^2+417x-207=0
a = 44; b = 417; c = -207;
Δ = b2-4ac
Δ = 4172-4·44·(-207)
Δ = 210321
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{210321}=\sqrt{9*23369}=\sqrt{9}*\sqrt{23369}=3\sqrt{23369}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(417)-3\sqrt{23369}}{2*44}=\frac{-417-3\sqrt{23369}}{88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(417)+3\sqrt{23369}}{2*44}=\frac{-417+3\sqrt{23369}}{88} $
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