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(7x-10)(2x+1)=90
We move all terms to the left:
(7x-10)(2x+1)-(90)=0
We multiply parentheses ..
(+14x^2+7x-20x-10)-90=0
We get rid of parentheses
14x^2+7x-20x-10-90=0
We add all the numbers together, and all the variables
14x^2-13x-100=0
a = 14; b = -13; c = -100;
Δ = b2-4ac
Δ = -132-4·14·(-100)
Δ = 5769
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5769}=\sqrt{9*641}=\sqrt{9}*\sqrt{641}=3\sqrt{641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{641}}{2*14}=\frac{13-3\sqrt{641}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{641}}{2*14}=\frac{13+3\sqrt{641}}{28} $
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