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7x(x-1)=3x+19
We move all terms to the left:
7x(x-1)-(3x+19)=0
We multiply parentheses
7x^2-7x-(3x+19)=0
We get rid of parentheses
7x^2-7x-3x-19=0
We add all the numbers together, and all the variables
7x^2-10x-19=0
a = 7; b = -10; c = -19;
Δ = b2-4ac
Δ = -102-4·7·(-19)
Δ = 632
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{158}}{2*7}=\frac{10-2\sqrt{158}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{158}}{2*7}=\frac{10+2\sqrt{158}}{14} $
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