16x^2+10x^2-8x+7=13

Solution for 16x^2+10x^2-8x+7=13 equation:

16x^2+10x^2-8x+7=13

We move all terms to the left:

16x^2+10x^2-8x+7-(13)=0

We add all the numbers together, and all the variables

26x^2-8x-6=0

a = 26; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·26·(-6)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{43}}{2*26}=\frac{8-4\sqrt{43}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{43}}{2*26}=\frac{8+4\sqrt{43}}{52}
$