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2x(x+7)=54
We move all terms to the left:
2x(x+7)-(54)=0
We multiply parentheses
2x^2+14x-54=0
a = 2; b = 14; c = -54;
Δ = b2-4ac
Δ = 142-4·2·(-54)
Δ = 628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{157}}{2*2}=\frac{-14-2\sqrt{157}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{157}}{2*2}=\frac{-14+2\sqrt{157}}{4} $
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