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3x(2x-11)-4(x-7)=5x-10
We move all terms to the left:
3x(2x-11)-4(x-7)-(5x-10)=0
We multiply parentheses
6x^2-33x-4x-(5x-10)+28=0
We get rid of parentheses
6x^2-33x-4x-5x+10+28=0
We add all the numbers together, and all the variables
6x^2-42x+38=0
a = 6; b = -42; c = +38;
Δ = b2-4ac
Δ = -422-4·6·38
Δ = 852
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{213}}{2*6}=\frac{42-2\sqrt{213}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{213}}{2*6}=\frac{42+2\sqrt{213}}{12} $
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