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(5x+4)(7x-2)=134
We move all terms to the left:
(5x+4)(7x-2)-(134)=0
We multiply parentheses ..
(+35x^2-10x+28x-8)-134=0
We get rid of parentheses
35x^2-10x+28x-8-134=0
We add all the numbers together, and all the variables
35x^2+18x-142=0
a = 35; b = 18; c = -142;
Δ = b2-4ac
Δ = 182-4·35·(-142)
Δ = 20204
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20204}=\sqrt{4*5051}=\sqrt{4}*\sqrt{5051}=2\sqrt{5051}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{5051}}{2*35}=\frac{-18-2\sqrt{5051}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{5051}}{2*35}=\frac{-18+2\sqrt{5051}}{70} $
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