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(2x+1)(5x-5)=130
We move all terms to the left:
(2x+1)(5x-5)-(130)=0
We multiply parentheses ..
(+10x^2-10x+5x-5)-130=0
We get rid of parentheses
10x^2-10x+5x-5-130=0
We add all the numbers together, and all the variables
10x^2-5x-135=0
a = 10; b = -5; c = -135;
Δ = b2-4ac
Δ = -52-4·10·(-135)
Δ = 5425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{217}}{2*10}=\frac{5-5\sqrt{217}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{217}}{2*10}=\frac{5+5\sqrt{217}}{20} $
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