8x^2-7=-26x

Solution for 8x^2-7=-26x equation:

8x^2-7=-26x

We move all terms to the left:

8x^2-7-(-26x)=0

We get rid of parentheses

8x^2+26x-7=0

a = 8; b = 26; c = -7;
Δ = b2-4ac
Δ = 262-4·8·(-7)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-30}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+30}{2*8}=\frac{4}{16}
=1/4
$