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5x(x+7)=14x-7
We move all terms to the left:
5x(x+7)-(14x-7)=0
We multiply parentheses
5x^2+35x-(14x-7)=0
We get rid of parentheses
5x^2+35x-14x+7=0
We add all the numbers together, and all the variables
5x^2+21x+7=0
a = 5; b = 21; c = +7;
Δ = b2-4ac
Δ = 212-4·5·7
Δ = 301
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{301}}{2*5}=\frac{-21-\sqrt{301}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{301}}{2*5}=\frac{-21+\sqrt{301}}{10} $
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