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5x^2+x=-4x+83
We move all terms to the left:
5x^2+x-(-4x+83)=0
We get rid of parentheses
5x^2+x+4x-83=0
We add all the numbers together, and all the variables
5x^2+5x-83=0
a = 5; b = 5; c = -83;
Δ = b2-4ac
Δ = 52-4·5·(-83)
Δ = 1685
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{-(5)-\sqrt{1685}}{2*5}=\frac{-5-\sqrt{1685}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1685}}{2*5}=\frac{-5+\sqrt{1685}}{10} $
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