8x^2-10x-3x^2/7-43x=0

Solution for 8x^2-10x-3x^2/7-43x=0 equation:

8x^2-10x-3x^2/7-43x=0

We add all the numbers together, and all the variables

8x^2-3x^2/7-53x=0

We multiply all the terms by the denominator


-3x^2+8x^2*7-53x*7=0

Wy multiply elements

-3x^2+56x^2-371x=0

We add all the numbers together, and all the variables

53x^2-371x=0

a = 53; b = -371; c = 0;
Δ = b2-4ac
Δ = -3712-4·53·0
Δ = 137641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{137641}=371$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-371)-371}{2*53}=\frac{0}{106}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-371)+371}{2*53}=\frac{742}{106}
=7
$