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10x^2+15x+7=1-2x
We move all terms to the left:
10x^2+15x+7-(1-2x)=0
We add all the numbers together, and all the variables
10x^2+15x-(-2x+1)+7=0
We get rid of parentheses
10x^2+15x+2x-1+7=0
We add all the numbers together, and all the variables
10x^2+17x+6=0
a = 10; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·10·6
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*10}=\frac{-24}{20} =-1+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*10}=\frac{-10}{20} =-1/2 $
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