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81x^2+63x+49+(8x+7)(-27x-21)=0
We multiply parentheses ..
81x^2+(-216x^2-168x-189x-147)+63x+49=0
We get rid of parentheses
81x^2-216x^2-168x-189x+63x-147+49=0
We add all the numbers together, and all the variables
-135x^2-294x-98=0
a = -135; b = -294; c = -98;
Δ = b2-4ac
Δ = -2942-4·(-135)·(-98)
Δ = 33516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33516}=\sqrt{1764*19}=\sqrt{1764}*\sqrt{19}=42\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-42\sqrt{19}}{2*-135}=\frac{294-42\sqrt{19}}{-270} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+42\sqrt{19}}{2*-135}=\frac{294+42\sqrt{19}}{-270} $
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