8x^2+14x-15=4/5

Solution for 8x^2+14x-15=4/5 equation:

8x^2+14x-15=4/5

We move all terms to the left:

8x^2+14x-15-(4/5)=0

We add all the numbers together, and all the variables

8x^2+14x-15-(+4/5)=0

We get rid of parentheses

8x^2+14x-15-4/5=0

We multiply all the terms by the denominator


8x^2*5+14x*5-4-15*5=0

We add all the numbers together, and all the variables

8x^2*5+14x*5-79=0

Wy multiply elements

40x^2+70x-79=0

a = 40; b = 70; c = -79;
Δ = b2-4ac
Δ = 702-4·40·(-79)
Δ = 17540
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:

$\sqrt{\Delta}=\sqrt{17540}=\sqrt{4*4385}=\sqrt{4}*\sqrt{4385}=2\sqrt{4385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{4385}}{2*40}=\frac{-70-2\sqrt{4385}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{4385}}{2*40}=\frac{-70+2\sqrt{4385}}{80}
$