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(2x-1)=(7x-19)(x+10)
We move all terms to the left:
(2x-1)-((7x-19)(x+10))=0
We get rid of parentheses
2x-((7x-19)(x+10))-1=0
We multiply parentheses ..
-((+7x^2+70x-19x-190))+2x-1=0
We calculate terms in parentheses: -((+7x^2+70x-19x-190)), so:We add all the numbers together, and all the variables
(+7x^2+70x-19x-190)
We get rid of parentheses
7x^2+70x-19x-190
We add all the numbers together, and all the variables
7x^2+51x-190
Back to the equation:
-(7x^2+51x-190)
2x-(7x^2+51x-190)-1=0
We get rid of parentheses
-7x^2+2x-51x+190-1=0
We add all the numbers together, and all the variables
-7x^2-49x+189=0
a = -7; b = -49; c = +189;
Δ = b2-4ac
Δ = -492-4·(-7)·189
Δ = 7693
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7693}=\sqrt{49*157}=\sqrt{49}*\sqrt{157}=7\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-7\sqrt{157}}{2*-7}=\frac{49-7\sqrt{157}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+7\sqrt{157}}{2*-7}=\frac{49+7\sqrt{157}}{-14} $
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