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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 = 81
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*2}=\frac{-24}{4} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*2}=\frac{-6}{4} =-1+1/2 $
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