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(4x-7)(7x-61)=180
We move all terms to the left:
(4x-7)(7x-61)-(180)=0
We multiply parentheses ..
(+28x^2-244x-49x+427)-180=0
We get rid of parentheses
28x^2-244x-49x+427-180=0
We add all the numbers together, and all the variables
28x^2-293x+247=0
a = 28; b = -293; c = +247;
Δ = b2-4ac
Δ = -2932-4·28·247
Δ = 58185
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{58185}=\sqrt{9*6465}=\sqrt{9}*\sqrt{6465}=3\sqrt{6465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-293)-3\sqrt{6465}}{2*28}=\frac{293-3\sqrt{6465}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-293)+3\sqrt{6465}}{2*28}=\frac{293+3\sqrt{6465}}{56} $
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