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0=x^2+7x-0.75
We move all terms to the left:
0-(x^2+7x-0.75)=0
We add all the numbers together, and all the variables
-(x^2+7x-0.75)=0
We get rid of parentheses
-x^2-7x+0.75=0
We add all the numbers together, and all the variables
-1x^2-7x+0.75=0
a = -1; b = -7; c = +0.75;
Δ = b2-4ac
Δ = -72-4·(-1)·0.75
Δ = 52
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-2\sqrt{13}}{2*-1}=\frac{7-2\sqrt{13}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+2\sqrt{13}}{2*-1}=\frac{7+2\sqrt{13}}{-2} $
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