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3x-2x(x-1)=-4x+7x-15
We move all terms to the left:
3x-2x(x-1)-(-4x+7x-15)=0
We add all the numbers together, and all the variables
3x-2x(x-1)-(3x-15)=0
We multiply parentheses
-2x^2+3x+2x-(3x-15)=0
We get rid of parentheses
-2x^2+3x+2x-3x+15=0
We add all the numbers together, and all the variables
-2x^2+2x+15=0
a = -2; b = 2; c = +15;
Δ = b2-4ac
Δ = 22-4·(-2)·15
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*-2}=\frac{-2-2\sqrt{31}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*-2}=\frac{-2+2\sqrt{31}}{-4} $
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