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(x+7)(-x+20)=3x-29
We move all terms to the left:
(x+7)(-x+20)-(3x-29)=0
We add all the numbers together, and all the variables
(x+7)(-1x+20)-(3x-29)=0
We get rid of parentheses
(x+7)(-1x+20)-3x+29=0
We multiply parentheses ..
(-1x^2+20x-7x+140)-3x+29=0
We get rid of parentheses
-1x^2+20x-7x-3x+140+29=0
We add all the numbers together, and all the variables
-1x^2+10x+169=0
a = -1; b = 10; c = +169;
Δ = b2-4ac
Δ = 102-4·(-1)·169
Δ = 776
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{194}}{2*-1}=\frac{-10-2\sqrt{194}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{194}}{2*-1}=\frac{-10+2\sqrt{194}}{-2} $
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