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5x^2+-44x+120=-30+11x
We move all terms to the left:
5x^2+-44x+120-(-30+11x)=0
We add all the numbers together, and all the variables
5x^2-44x-(11x-30)+120+=0
We add all the numbers together, and all the variables
5x^2-44x-(11x-30)=0
We get rid of parentheses
5x^2-44x-11x+30=0
We add all the numbers together, and all the variables
5x^2-55x+30=0
a = 5; b = -55; c = +30;
Δ = b2-4ac
Δ = -552-4·5·30
Δ = 2425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{97}}{2*5}=\frac{55-5\sqrt{97}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{97}}{2*5}=\frac{55+5\sqrt{97}}{10} $
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