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5x(x+7)=2x-10
We move all terms to the left:
5x(x+7)-(2x-10)=0
We multiply parentheses
5x^2+35x-(2x-10)=0
We get rid of parentheses
5x^2+35x-2x+10=0
We add all the numbers together, and all the variables
5x^2+33x+10=0
a = 5; b = 33; c = +10;
Δ = b2-4ac
Δ = 332-4·5·10
Δ = 889
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{-(33)-\sqrt{889}}{2*5}=\frac{-33-\sqrt{889}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{889}}{2*5}=\frac{-33+\sqrt{889}}{10} $
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