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15x^2+67x=18x+150
We move all terms to the left:
15x^2+67x-(18x+150)=0
We get rid of parentheses
15x^2+67x-18x-150=0
We add all the numbers together, and all the variables
15x^2+49x-150=0
a = 15; b = 49; c = -150;
Δ = b2-4ac
Δ = 492-4·15·(-150)
Δ = 11401
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{11401}}{2*15}=\frac{-49-\sqrt{11401}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{11401}}{2*15}=\frac{-49+\sqrt{11401}}{30} $
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