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7x(5x+14)=104
We move all terms to the left:
7x(5x+14)-(104)=0
We multiply parentheses
35x^2+98x-104=0
a = 35; b = 98; c = -104;
Δ = b2-4ac
Δ = 982-4·35·(-104)
Δ = 24164
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24164}=\sqrt{4*6041}=\sqrt{4}*\sqrt{6041}=2\sqrt{6041}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{6041}}{2*35}=\frac{-98-2\sqrt{6041}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{6041}}{2*35}=\frac{-98+2\sqrt{6041}}{70} $
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