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x^2+7x-53=11/3
We move all terms to the left:
x^2+7x-53-(11/3)=0
We add all the numbers together, and all the variables
x^2+7x-53-(+11/3)=0
We get rid of parentheses
x^2+7x-53-11/3=0
We multiply all the terms by the denominator
x^2*3+7x*3-11-53*3=0
We add all the numbers together, and all the variables
x^2*3+7x*3-170=0
Wy multiply elements
3x^2+21x-170=0
a = 3; b = 21; c = -170;
Δ = b2-4ac
Δ = 212-4·3·(-170)
Δ = 2481
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{-(21)-\sqrt{2481}}{2*3}=\frac{-21-\sqrt{2481}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{2481}}{2*3}=\frac{-21+\sqrt{2481}}{6} $
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