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2x(x+10)=5x+18
We move all terms to the left:
2x(x+10)-(5x+18)=0
We multiply parentheses
2x^2+20x-(5x+18)=0
We get rid of parentheses
2x^2+20x-5x-18=0
We add all the numbers together, and all the variables
2x^2+15x-18=0
a = 2; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·2·(-18)
Δ = 369
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*2}=\frac{-15-3\sqrt{41}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*2}=\frac{-15+3\sqrt{41}}{4} $
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