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X^2+5X-27=-10X+7
We move all terms to the left:
X^2+5X-27-(-10X+7)=0
We get rid of parentheses
X^2+5X+10X-7-27=0
We add all the numbers together, and all the variables
X^2+15X-34=0
a = 1; b = 15; c = -34;
Δ = b2-4ac
Δ = 152-4·1·(-34)
Δ = 361
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{361}=19$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-19}{2*1}=\frac{-34}{2} =-17 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+19}{2*1}=\frac{4}{2} =2 $
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