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15x^2-38x-18=6-7x
We move all terms to the left:
15x^2-38x-18-(6-7x)=0
We add all the numbers together, and all the variables
15x^2-38x-(-7x+6)-18=0
We get rid of parentheses
15x^2-38x+7x-6-18=0
We add all the numbers together, and all the variables
15x^2-31x-24=0
a = 15; b = -31; c = -24;
Δ = b2-4ac
Δ = -312-4·15·(-24)
Δ = 2401
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{2401}=49$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-49}{2*15}=\frac{-18}{30} =-3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+49}{2*15}=\frac{80}{30} =2+2/3 $
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