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2x(x+5)=102
We move all terms to the left:
2x(x+5)-(102)=0
We multiply parentheses
2x^2+10x-102=0
a = 2; b = 10; c = -102;
Δ = b2-4ac
Δ = 102-4·2·(-102)
Δ = 916
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{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{229}}{2*2}=\frac{-10-2\sqrt{229}}{4}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{229}}{2*2}=\frac{-10+2\sqrt{229}}{4}
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