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(x+7)(x-2)=x+1
We move all terms to the left:
(x+7)(x-2)-(x+1)=0
We get rid of parentheses
(x+7)(x-2)-x-1=0
We multiply parentheses ..
(+x^2-2x+7x-14)-x-1=0
We add all the numbers together, and all the variables
(+x^2-2x+7x-14)-1x-1=0
We get rid of parentheses
x^2-2x+7x-1x-14-1=0
We add all the numbers together, and all the variables
x^2+4x-15=0
a = 1; b = 4; c = -15;
Δ = b2-4ac
Δ = 42-4·1·(-15)
Δ = 76
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{19}}{2*1}=\frac{-4-2\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{19}}{2*1}=\frac{-4+2\sqrt{19}}{2} $
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