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2x-4x(x-2)=-6+5x-7
We move all terms to the left:
2x-4x(x-2)-(-6+5x-7)=0
We add all the numbers together, and all the variables
2x-4x(x-2)-(5x-13)=0
We multiply parentheses
-4x^2+2x+8x-(5x-13)=0
We get rid of parentheses
-4x^2+2x+8x-5x+13=0
We add all the numbers together, and all the variables
-4x^2+5x+13=0
a = -4; b = 5; c = +13;
Δ = b2-4ac
Δ = 52-4·(-4)·13
Δ = 233
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{233}}{2*-4}=\frac{-5-\sqrt{233}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{233}}{2*-4}=\frac{-5+\sqrt{233}}{-8} $
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