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2x(3x-5)-4x=2x-7
We move all terms to the left:
2x(3x-5)-4x-(2x-7)=0
We add all the numbers together, and all the variables
-4x+2x(3x-5)-(2x-7)=0
We multiply parentheses
6x^2-4x-10x-(2x-7)=0
We get rid of parentheses
6x^2-4x-10x-2x+7=0
We add all the numbers together, and all the variables
6x^2-16x+7=0
a = 6; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·6·7
Δ = 88
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{22}}{2*6}=\frac{16-2\sqrt{22}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{22}}{2*6}=\frac{16+2\sqrt{22}}{12} $
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