8x^2-65x-63=(5x+3)

Solution for 8x^2-65x-63=(5x+3) equation:

8x^2-65x-63=(5x+3)

We move all terms to the left:

8x^2-65x-63-((5x+3))=0


We calculate terms in parentheses: -((5x+3)), so:

(5x+3)

We get rid of parentheses

5x+3

Back to the equation:

-(5x+3)


We get rid of parentheses

8x^2-65x-5x-3-63=0

We add all the numbers together, and all the variables

8x^2-70x-66=0

a = 8; b = -70; c = -66;
Δ = b2-4ac
Δ = -702-4·8·(-66)
Δ = 7012
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:

$\sqrt{\Delta}=\sqrt{7012}=\sqrt{4*1753}=\sqrt{4}*\sqrt{1753}=2\sqrt{1753}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1753}}{2*8}=\frac{70-2\sqrt{1753}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1753}}{2*8}=\frac{70+2\sqrt{1753}}{16}
$