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3x(2x-7)-4x(5-2x)=3x+3
We move all terms to the left:
3x(2x-7)-4x(5-2x)-(3x+3)=0
We add all the numbers together, and all the variables
3x(2x-7)-4x(-2x+5)-(3x+3)=0
We multiply parentheses
6x^2+8x^2-21x-20x-(3x+3)=0
We get rid of parentheses
6x^2+8x^2-21x-20x-3x-3=0
We add all the numbers together, and all the variables
14x^2-44x-3=0
a = 14; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·14·(-3)
Δ = 2104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{526}}{2*14}=\frac{44-2\sqrt{526}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{526}}{2*14}=\frac{44+2\sqrt{526}}{28} $
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