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-5x^2+6x+7=x^2-4x
We move all terms to the left:
-5x^2+6x+7-(x^2-4x)=0
We get rid of parentheses
-5x^2-x^2+6x+4x+7=0
We add all the numbers together, and all the variables
-6x^2+10x+7=0
a = -6; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-6)·7
Δ = 268
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{67}}{2*-6}=\frac{-10-2\sqrt{67}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{67}}{2*-6}=\frac{-10+2\sqrt{67}}{-12} $
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