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-6(-2x-9)x1=9x+50
We move all terms to the left:
-6(-2x-9)x1-(9x+50)=0
We multiply parentheses
12x^2+54x-(9x+50)=0
We get rid of parentheses
12x^2+54x-9x-50=0
We add all the numbers together, and all the variables
12x^2+45x-50=0
a = 12; b = 45; c = -50;
Δ = b2-4ac
Δ = 452-4·12·(-50)
Δ = 4425
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{4425}=\sqrt{25*177}=\sqrt{25}*\sqrt{177}=5\sqrt{177}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{177}}{2*12}=\frac{-45-5\sqrt{177}}{24}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{177}}{2*12}=\frac{-45+5\sqrt{177}}{24}
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