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-11x+2x(x-3)+7x=5x-6
We move all terms to the left:
-11x+2x(x-3)+7x-(5x-6)=0
We add all the numbers together, and all the variables
-4x+2x(x-3)-(5x-6)=0
We multiply parentheses
2x^2-4x-6x-(5x-6)=0
We get rid of parentheses
2x^2-4x-6x-5x+6=0
We add all the numbers together, and all the variables
2x^2-15x+6=0
a = 2; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·2·6
Δ = 177
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{-(-15)-\sqrt{177}}{2*2}=\frac{15-\sqrt{177}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{177}}{2*2}=\frac{15+\sqrt{177}}{4} $
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