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7(x-11)3x=-53
We move all terms to the left:
7(x-11)3x-(-53)=0
We add all the numbers together, and all the variables
7(x-11)3x+53=0
We multiply parentheses
21x^2-231x+53=0
a = 21; b = -231; c = +53;
Δ = b2-4ac
Δ = -2312-4·21·53
Δ = 48909
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{-(-231)-\sqrt{48909}}{2*21}=\frac{231-\sqrt{48909}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-231)+\sqrt{48909}}{2*21}=\frac{231+\sqrt{48909}}{42} $
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