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5x(9+x)=70
We move all terms to the left:
5x(9+x)-(70)=0
We add all the numbers together, and all the variables
5x(x+9)-70=0
We multiply parentheses
5x^2+45x-70=0
a = 5; b = 45; c = -70;
Δ = b2-4ac
Δ = 452-4·5·(-70)
Δ = 3425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3425}=\sqrt{25*137}=\sqrt{25}*\sqrt{137}=5\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{137}}{2*5}=\frac{-45-5\sqrt{137}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{137}}{2*5}=\frac{-45+5\sqrt{137}}{10} $
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