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3x-(2x-7)3x=15
We move all terms to the left:
3x-(2x-7)3x-(15)=0
We multiply parentheses
-6x^2+3x+21x-15=0
We add all the numbers together, and all the variables
-6x^2+24x-15=0
a = -6; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·(-6)·(-15)
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{6}}{2*-6}=\frac{-24-6\sqrt{6}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{6}}{2*-6}=\frac{-24+6\sqrt{6}}{-12} $
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