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(14x-10)(8x+5)+4=180
We move all terms to the left:
(14x-10)(8x+5)+4-(180)=0
We add all the numbers together, and all the variables
(14x-10)(8x+5)-176=0
We multiply parentheses ..
(+112x^2+70x-80x-50)-176=0
We get rid of parentheses
112x^2+70x-80x-50-176=0
We add all the numbers together, and all the variables
112x^2-10x-226=0
a = 112; b = -10; c = -226;
Δ = b2-4ac
Δ = -102-4·112·(-226)
Δ = 101348
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{101348}=\sqrt{4*25337}=\sqrt{4}*\sqrt{25337}=2\sqrt{25337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{25337}}{2*112}=\frac{10-2\sqrt{25337}}{224} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{25337}}{2*112}=\frac{10+2\sqrt{25337}}{224} $
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