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7x(2x-5)=12x-3-3x
We move all terms to the left:
7x(2x-5)-(12x-3-3x)=0
We add all the numbers together, and all the variables
7x(2x-5)-(9x-3)=0
We multiply parentheses
14x^2-35x-(9x-3)=0
We get rid of parentheses
14x^2-35x-9x+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 = 1768
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1768}=\sqrt{4*442}=\sqrt{4}*\sqrt{442}=2\sqrt{442}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{442}}{2*14}=\frac{44-2\sqrt{442}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{442}}{2*14}=\frac{44+2\sqrt{442}}{28} $
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